Transverse & longitudinal waves

 Waves can come in one of two types:

o Transverse waves
o Longitudinal waves

Transverse waves

 Transverse waves are defined as:

Waves that vibrate or oscillate perpendicular to the direction of energy transfer

 Transverse waves:
o oscillate perpendicularly to the direction of travel
o transfer energy, but not the particles of the medium
o exist as mechanical waves which can travel in solids and on the surfaces
of liquids but not through liquids or gases
o exist as electromagnetic waves which can move in solids, liquids, gases
and in a vacuum

 On a transverse wave:
o the highest point above the rest position is called a peak, or crest
o the lowest point below the rest position is called a trough

Example of a transverse wave

Transverse waves can be seen in a rope when it is moved quickly up and down

 Examples of transverse waves are:

o Ripples on the surface of water
o Vibrations in a guitar string
o S-waves (a type of seismic wave)
o Electromagnetic waves (such as radio, light, X-rays etc)
Longitudinal waves

 Longitudinal waves are defined as:

Waves where the points along its length vibrate parallel to the direction of energy
transfer

 Longitudinal waves:
o Oscillate in the same direction as the direction of wave travel
o Transfer energy, but not the particles of the medium
o Move in solids, liquids and gases
o Cannot move in a vacuum (since there are no particles)

 The key features of a longitudinal wave are where the points are:
o Close together, called compressions
o Spaced apart, called rarefactions

Example of a longitudinal wave

Longitudinal waves can be seen in a slinky spring when it is moved quickly

backwards and forwards

 Examples of longitudinal waves are:

o Sound waves
o P-waves (a type of seismic wave)
o Pressure waves caused by repeated movements in a liquid or gas

Comparing transverse & longitudinal waves

 Wave vibrations can be shown on ropes (transverse) and springs (longitudinal)

A comparison of longitudinal and transverse waves

 Waves can be shown through vibrations in ropes or springs

Properties of transverse and longitudinal waves

Property Transverse Waves Longitudinal Waves

Structure Peaks and troughs Compressions and rarefactions
Vibration Perpendicular to the direction of energy transfer Parallel to the direction of energy transfer
Vacuum Can travel in a vacuum (electromagnetic waves) Cannot travel in a vacuum
Material Can travel through solids, and on the surface of liquids Can travel through solids, liquids and gases
Density Constant density Changes in density
Pressure Pressure is constant Changes in pressure
Speed of Dependent on material it is travelling through (fastest in Dependent on material it is travelling through
wave a vacuum) (fastest in a solid)
Waves & energy
 Waves are disturbances caused by an oscillating source that
transfer energy and information without transferring matter
 Waves are described as oscillations or vibrations about a fixed point
o For example, ripples cause particles of water to oscillate up and down
o Sound waves cause particles of air to vibrate back and forth

Evidence that waves transfer energy and not matter

 Waves transfer energy and information, but not matter. This toy duck bobs up
and down as water waves pass underneath

 The wave on the surface of a body of water is a transverse wave

 The duck moves perpendicular to the direction of the wave
o The duck moves up and down but does not travel with the wave

Describing wave motion

 When describing wave motion, there are several terms which are important to
know, including:
o Amplitude (A)
o Wavelength (λ)
o Frequency (f)
o Time Period (T)

Amplitude (A)

 Amplitude is defined as:

Amplitude is the maximum or minimum displacement from the undisturbed

position

 The maximum displacement of a wave is the peak

 The minimum displacement of a wave is the trough
 Amplitude is measured in metres (m)

Wavelength (λ)

 Wavelength is defined as

The distance from one point on the wave to the same point on the next wave

 In a transverse wave:
o The wavelength can be measured from one peak to the next peak
 In a longitudinal wave:
o The wavelength can be measured from the centre of one compression to
the centre of the next
 Wavelength is measured in metres (m)

Graphical representation of transverse waves

 The amplitude and wavelength of a transverse wave can be represented

graphically
 The distance along a wave is typically put on the x-axis of a wave diagram
A diagram of a transverse wave

Diagram showing the amplitude and wavelength of a transverse wave

 The wavelength is given the symbol λ (lambda) and is measured in metres (m)

Diagram showing the amplitude and wavelength of a transverse wave

 The wavelength is given the symbol λ (lambda) and is measured in metres (m)
 The distance along a wave is typically put on the x-axis of a wave diagram

Frequency (f)

 Frequency is defined as:

The number of waves passing a point in a second

 Frequency is measured in hertz (Hz)

o The unit hertz is equivalent to 'per second'
o 5 Hz = 5 waves per second
 Waves with a higher frequency transfer a higher amount of energy

Time Period (T)

 The time period (or sometimes just 'period') of a wave is defined as:

The time taken for a single wave to pass a point

 The period is measured in seconds (s)

 The equation linking frequency and time period is explained in Frequency & time
period
Formula triangle for the wave speed equation

A formula triangle can be used to help rearrange the wave speed equation

 For more information on how to use a formula triangle refer to the revision note
on Speed

Frequency & time period

 Frequency and time period are defined in Describing wave motion
 The following equation relates time period and frequency:

Calculations in different contexts

  The wave equation can be applied and rearranged to calculate the properties
of Transverse and longitudinal waves
 The wave equation applies to all types of waves,
including Sound waves and Electromagnetic waves

The Doppler effect

 The Doppler effect is defined as:

The apparent change in observed wavelength and frequency of a wave emitted by

a moving source relative to an observer

 The Doppler effect can be observed whenever sources of waves move

o The frequency of the sound waves emitted by ambulance or police sirens
goes from a high pitch (high frequency) to a low pitch (low frequency) as
the vehicle whizzes past
o Galaxies in outer space emit light waves which appear redder (longer
wavelength) to an observer on Earth because the stars are
moving away from us

Explaining the Doppler effect

 Usually, when a stationary object emits waves, the waves spread

out symmetrically

A stationary source of sound waves

This stationary police car emits sound from the siren and the waves spread out
symmetrically

 To an observer standing in front of an object moving towards them:

o The waves appear to get squashed together because the wavelength
appears to get shorter (and the frequency appears to get higher)
 To an observer standing behind an object moving away from them:
 o The waves appear to get stretched apart because the wavelength
appears to get longer (and the frequency appears to get lower)

The Doppler effect is observed when the source of the sound waves is moving

To an observer in front of the moving car, the wavelength appears smaller

because they squash together. To an observer behind the moving car, the waves
appear to stretch out
Properties of em waves
 Light is part of a continuous electromagnetic spectrum that consists of the
following types of radiation:
o radio
o microwave
o infrared
o visible
o ultraviolet
o x-ray
o gamma ray
 All waves in the electromagnetic spectrum share the following properties:
o They are all transverse
o They can all travel through free space (a vacuum)
o They all travel at the same speed in free space

The EM spectrum
 The types of radiation found in the electromagnetic spectrum have a specific
order based on their wavelength (and frequency)
 This order listed above has:
 o Radio waves at the top because they have the longest
wavelength (and highest frequency)
o Gamma rays at the bottom because they have the shortest
wavelength (and lowest frequency)
 Wavelength and frequency are inversely proportional to each other:
o An increase in wavelength is a decrease in frequency (towards the red
end of the spectrum)
o A decrease in wavelength is an increase in frequency (towards the violet
end of the spectrum)
o This is explained by the Wave equation

The types of radiation in the EM spectrum from longest to shortest wavelength

Visible light is just one small part of a much bigger spectrum: The
electromagnetic spectrum

Visible Spectrum

 Visible light is the only part of the EM spectrum detectable by the human eye
o However, it is only a very small part of the whole electromagnetic
spectrum
o In the natural world, many animals, such as birds, bees and certain fish,
can perceive beyond visible light and use infra-red and UV wavelengths of
light to see

 Each colour within the visible light spectrum corresponds to a narrow band
of wavelength and frequency
 The different colours of waves correspond to different wavelengths:
o Red has the longest wavelength (and the lowest frequency)
 o Violet has the shortest wavelength (and the highest frequency)

The colours of the visible spectrum

The colours of the visible spectrum: red has the longest wavelength; violet has
the shortest
Applications of EM waves
 Each region of the electromagnetic spectrum has a variety of uses and
applications

Uses of EM waves

Wave Type Uses

Radio Broadcasting and communications
Microwaves Cooking and satellite transmissions
Infrared Heaters and night vision equipment
Visible light Optical fibres and photography
Ultraviolet Fluorescent lamps
X-rays Observing the internal structure of objects and materials, including medical applications
Gamma rays Sterilising food and medical equipment
Radio waves & microwaves

 Both radio waves and microwaves are used in wireless communication

 This includes:
o Radios
o Air traffic communication
o Mobile phone communication
 At very high intensities microwaves are used to heat things in a microwave
oven

Infrared

 Infrared is emitted by warm objects and can be detected using special cameras
(thermal imaging cameras).
  Examples of the uses of infrared are:
o Security cameras to see people in the dark
o TV remote controls
o Transport signals down fibre optic cables

Visible

 Visible light is the only part of the electromagnetic spectrum that the human
eye can see
 It is also used in fibre optic communication

Ultraviolet

 Ultraviolet is responsible for giving you a sun tan, which is your body’s way of
protecting itself against the ultraviolet
 When certain substances are exposed to ultraviolet, they absorb it and re-emit it
as visible light (making them glow)
o This process is known as fluorescence
 Fluorescence can be used to secretly mark things in special ink, such as
banknotes

X-rays

 The most obvious use of x-rays is in medicine

 X-rays can pass through most body tissues but are absorbed by the denser parts
of the body, such as bones

Gamma Rays

 Gamma rays are dangerous and can be used to kill cells and living tissue
 Gamma rays can also be used to sterilise equipment by killing off the bacteria

Dangers of EM waves
Risks of excessive exposure to EM radiation

 Excessive exposure of the human body to electromagnetic waves can have

detrimental effects
 Risks from overexposure to certain wavelengths include:
o microwaves can cause heat damage to internal organs due to the
internal heating of body tissue
o infrared can burn the skin
o ultraviolet can damage skin cells causing sunburn and blindness
o gamma and X-rays can kill cells causing cancer and cell mutations
Dangers and uses of each part of the EM spectrum

Uses and dangers of the electromagnetic spectrum

 As discussed in Describing wave motion as the frequency of electromagnetic

(EM) waves increases, so does the energy
 Beyond the visible part of the EM spectrum, the energy becomes large enough
to ionise atoms
 As a result of this, the danger associated with EM waves increases along with
the frequency
o The shorter the wavelength, the more ionising the radiation
Protective measures against the risks of over-exposure

 Devices using hazardous EM radiation contain safety features that reduce

human exposure:
o microwaves from microwave ovens are prevented from escaping the
oven by the metal walls and metal grid in the glass door
o infrared wearing protective clothing such as gloves can prevent the skin
from feeling the hear
o ultraviolet ray damage to the eyes is reduced by
wearing sunglasses that absorb ultraviolet and prevent it from reaching
the eyes. Sunscreen also absorbs ultraviolet light preventing it from
damaging the skin.
o gamma and X-rays damage is reduced through using minimal levels in
medicine. Doctors leave the room during x-rays to avoid unnecessary
exposure. Radiographers wear radiation badges to measure their level of
radiation exposure. People working with gamma rays routinely have their
dose levels tested.

Radiation badges

Radiation badges are used by people working closely with radiation to monitor
exposure
Light
 Visible light is a part of the Electromagnetic spectrum which means it is
a transverse wave
o This is explained in Transverse & longitudinal waves

Representing a transverse wave

 Light waves are transverse: the particles vibrate in a perpendicular direction to
the energy transfer

 Light can undergo:

o Reflection
o Refraction

Sound
 Sound waves are longitudinal waves
o This is explained in Transverse & longitudinal waves

 Longitudinal waves are usually drawn as several lines to show that the wave is
moving parallel to the direction of energy transfer
o Drawing the lines closer together represents the compressions
o Drawing the lines further apart represents the rarefactions

Representing a longitudinal wave

 Longitudinal waves are represented as sets of lines with rarefactions and
compressions

 Sound can also undergo:

o Reflection
o Refraction
 The reflection of a sound wave is called an echo

Reflection & refraction

 All waves, whether transverse or longitudinal, can be reflected and refracted
 Reflection occurs when:

A wave hits a boundary between two media and does not pass through, but
instead stays in the original medium

 In optics the word medium is used to describe a material that transmits light
o Media means more than one medium

An example of reflection

An identical image of the tree is seen in the water due to reflection

 Refraction occurs when:

A wave passes a boundary between two different transparent media and

undergoes a change in direction

An example of refraction
 Waves can change direction when moving between materials with different
densities
The law of reflection
 The law of reflection states that:

Angle of incidence (i) = Angle of reflection (r)

 Angles are measured between the wave direction (ray) and a line at 90 degrees
to the boundary called the normal
o The angle of the wave approaching the boundary is called the angle of
incidence (i)
o The angle of the wave leaving the boundary is called the angle of
reflection (r)

An example of reflection in a plane mirror

Ray diagram of the reflection of a wave in a mirror

Ray diagrams
Reflection ray diagrams
  When drawing a ray diagram an arrow is used to show the direction the wave is
travelling
o An incident ray has an arrow pointing towards the boundary
o A reflected ray has an arrow pointing away from the boundary

A diagram showing the law of reflection

The angle of incidence and angle of reflection are equal in the law of reflection

Refraction ray diagrams

 The direction of the incident and refracted rays are also taken from
the normal line
 The change in direction of the refracted ray depends on the difference in density
between the two media:
o From less dense to more dense (e.g air to glass), light bends towards the
normal
o From more dense to less dense (e.g. glass to air), light bends away from
the normal
o When passing along the normal (perpendicular) the light does not
bend at all

A diagram of a ray refracted into and out of a glass block

 How to construct a ray diagram showing the refraction of light as it passes
through a rectangular block

 The change in direction occurs due to the change in speed when travelling in
different substances
o When light passes into a denser substance the rays will slow down,
hence they bend towards the normal

 The only properties that change during refraction are speed and wavelength –
the frequency of waves does not change
o Different frequencies account for different colours of light (red has a low
frequency, whilst blue has a high frequency)
o When light refracts, it does not change colour (think of a pencil in a
glass of water), therefore, the frequency does not change

Core practical 4: investigating refraction

Aim of the experiment

 To investigate the refraction of light using transparent rectangular blocks, semi-

circular blocks and triangular prisms
o To review your understanding of refraction use the revision note Reflection
& refraction

Variables

 Independent variable = shape of the block

 Dependent variable = direction of refraction
 Control variables:
o Width of the light beam
o Same frequency / wavelength of the light

Equipment list
 Equipment Purpose
To provide a narrow beam of light that can be easily
Ray Box
refracted
Protractor To measure the angles of incidence and refraction
Sheet of Paper To mark the lines indicating the incident and refracted rays
Pencil To draw the incident and refracted ray lines onto the paper
Ruler To draw the incident and refracted ray lines onto the paper
Perspex blocks (rectangular block, semi-circular block &
To refract the light beam
prism)
 Resolution of measuring equipment:
o Protractor = 1°
o Ruler = 1 mm

Method

Refraction experiment set up

Apparatus to investigate refraction

1. Place the glass block on a sheet of paper, and carefully draw around the
rectangular perspex block using a pencil
2. Switch on the ray box and direct a beam of light at the side face of the block
3. Mark on the paper:
 A point on the ray close to the ray box
 The point where the ray enters the block
 The point where the ray exits the block
 A point on the exit light ray which is a distance of about 5 cm away from
the block
4. Draw a dashed line normal (at right angles) to the outline of the block where the
points are
5. Remove the block and join the points marked with three straight lines
 6. Replace the block within its outline and repeat the above process for a ray
striking the block at a different angle
7. Repeat the procedure for each shape of perspex block (prism and semi-circular)

Results

 Consider the light paths through the different-shaped blocks

Refraction experiment results with different media

Refraction of light through different shapes of perspex blocks

 The final diagram for each shape will include multiple light ray paths for the
different angles of incidences (i) at which the light strikes the blocks
 This will help demonstrate how the angle of refraction (r) changes with the angle
of incidence
o Label these paths clearly with (1) (2) (3) or A, B, C to make these clearer
 Use the laws of refraction to analyse these results
o You can use the revision note Reflection & refraction to do this

Evaluating the experiment

Systematic Errors:

 An error could occur if the 90° lines are drawn incorrectly

o Use a set square to draw perpendicular lines

Random Errors:

 The points for the incoming and reflected beam may be inaccurately marked
 o Use a sharpened pencil and mark in the middle of the beam
 The protractor resolution may make it difficult to read the angles accurately
o Use a protractor with a higher resolution

Safety considerations

 The ray box light could cause burns if touched

o Run burns under cold running water for at least five minutes
 Looking directly into the light may damage the eyes
o Avoid looking directly at the light
o Stand behind the ray box during the experiment
 Keep all liquids away from the electrical equipment and paper

A formula triangle can help rearrange the snell's law equation

Snell's law formula triangle

 For more information on how to use a formula triangle refer to the revision note
on Speed

Refractive index
  The refractive index is a number which is related to the speed of light in the
material (which is always less than the speed of light in a vacuum):

Core practical 5: investigating snell's law

Aims of the experiment

 To investigate the refractive index of glass, using a glass block

Variables

 Independent variable = angle of incidence, i

 Dependent variable = angle of refraction , r
 Control variables:
o Use of the same perspex block
o Width of the light beam
o Same frequency / wavelength of the light

Equipment

Equipment list

Equipment Purpose
Ray Box To provide a narrow beam of light that can be easily refracted
Protractor To measure the angles of incidence and refraction
Sheet of Paper To mark the lines indicating the incident and refracted rays
Pencil To draw the incident and refracted ray lines onto the paper
Ruler To draw the incident and refracted ray lines onto the paper
Perspex rectangle To refract the light beam
 Resolution of measuring equipment:
o Protractor = 1°
o Ruler = 1 mm

Method
Diagram of equipment set up

Apparatus set-up to investigate Snell's Law

1. Place the glass block on a sheet of paper, and carefully draw around the block
using a pencil
2. Draw a dashed line normal (at right angles) to the outline of the block
3. Use a protractor to measure the angles of incidence to be studied and mark
these lines on the paper
4. Switch on the ray box and direct a beam of light at the side face of the block at
the first angle to be investigated
5. Mark on the paper:
 A point on the ray close to the ray box
 The point where the ray enters the block
 The point where the ray exits the block
 A point on the exit light ray which is a distance of about 5 cm away from
the block
6. Remove the block and join the points marked with three straight lines
7. Replace the block within its outline and repeat the above process for a rays
striking the block at the next angle

An example results table

Angle of incidence, i / ° Angle of refraction, r / °

0
10
20
30
40
50
60
70
80
Analysis of results
  If the angles have been measured correctly, the paper should end up looking like
this:

A diagram showing how to measure the angles of incidence and refraction

 Snell's Law relates the angles of incidence and refraction

o This is covered in the Snell's law revision note
 Plot a graph of sin i on the y-axis against sin r on the x-axis
o The refractive index is equal to the gradient of the graph

A graph of the results of snell's law experiment

Evaluating the experiment

Systematic Errors:

 An error could occur if the 90° lines are drawn incorrectly

o Use a set square to draw perpendicular lines

Random Errors:

 The points for the incoming and reflected beam may be inaccurately marked
o Use a sharpened pencil and mark in the middle of the beam
 The protractor resolution may make it difficult to read the angles accurately
o Use a protractor with a higher resolution

Safety considerations
  The ray box light could cause burns if touched
o Run burns under cold running water for at least five minute
 Looking directly into the light may damage the eyes
o Avoid looking directly at the light
o Stand behind the ray box during the experiment
 Keep all liquids away from the electrical equipment and paper

Total internal reflection

 Sometimes, when light is moving from a denser medium towards a less dense
one, instead of being refracted, all of the light is reflected
o This phenomenon is called total internal reflection

 Total internal reflection (TIR) occurs when:

The angle of incidence is greater than the critical angle and the incident material
is denser than the second material

 Therefore, the two conditions for total internal reflection are:

o The angle of incidence > the critical angle
o The incident material is denser than the second material

The angles of refraction, critical and total internal reflection

The critical angle is different for different materials. Refraction occurs when the
angle of incidence is less than the critical angle, and total internal reflection
occurs when it is greater

 Total internal reflection is utilised in

o optical fibres e.g. endoscopes
o prisms e.g. periscopes
Optical fibres

 Total internal reflection is used to reflect light along optical fibres, meaning they
can be used for
o communications
o endoscopes
o decorative lamps

 Light travelling down an optical fibre is totally internally reflected each time it hits
the edge of the fibre

Light travelling in an optical fibre

Optical fibres utilise total internal reflection for communications

Structure of an endoscope
 Endoscopes utilise total internal reflection to see inside a patient's body

Prisms

 Prisms are used in a variety of optical instruments, including

o periscopes
o binoculars
o telescopes
o cameras

 Prisms are also used in safety reflectors for bicycles and cars, as well as posts
marking the edges of roads
 A periscope is a device consisting of two right-angled prisms that can be used to
see over tall objects

Reflection of light in a periscope

 When light travels through a periscope, it totally internally reflects through
prisms causing the light to reflect at right angles

 The light totally internally reflects in both prisms

Reflection of light by right-angled prisms

Single and double reflection through right-angled prisms

Critical angle
 As the angle of incidence is increased, the angle of refraction also increases until
it gets closer to 90°
 When the angle of refraction is exactly 90° the light is refracted along the
boundary
o At this point, the angle of incidence is known as the critical angle c

Changing the angle of incidence to obtain the critical angle

 As the angle of incidence increases it will eventually surplus the critical angle
and lead to total internal reflection of the light

 When the angle of incidence is larger than the critical angle, the refracted ray is
now reflected
o This is total internal reflection

Core practical 6: investigating the speed of sound

Equipment

Equipment List

Equipment Purpose
Trundle Wheel To measure the distance travelled by the sound waves
Wooden Blocks To create a sound when banged together
Stopwatch To time how long it takes the sound waves to travel
Oscilloscope To display the sound wave electronically
Microphones x2 To detect sound waves and turn them into an electrical signal
Tape Measure To measure the distance between microphones
 Resolution of measuring equipment:
o Trundle wheel = 0.01 m
o Tape measure = 0.1 cm
o Stopwatch = 0.01 s

Experiment 1: measuring the speed of sound between two points

 The aim of this experiment is to measure the speed of sound in air between two
points

Variables

 Independent variable = Distance

 Dependent variable = Time
 Control variables:
o Same location to carry out the experiment

Method

Measuring the speed of sound in air

Measuring the speed of sound directly between two points

1. Use the trundle wheel to measure a distance of 100 m between two people
2. One of the people should have two wooden blocks, which they will bang together
above their head to generate sound waves
 3. The second person should have a stopwatch which they start when they see the
first person banging the blocks together and stop when they hear the sound
4. This should be repeated several times and an average taken for the time
travelled by the sound waves
5. Repeat this experiment for various distances, e.g. 120 m, 140 m, 160 m, 180 m

Results

An example results table for the speed of sound in air

Distance / m Time 1 / s Time 2 / s Time 3 / s Average time / s

100
120
140
160
180
Analysis of results

Experiment 2: measuring the speed of sound with oscilloscopes

 The aim of this experiment is to measure the speed of sound in air between two
points using an oscilloscope

Variables

 Independent variable = Distance

 Dependent variable = Time
 Control variables:
o Same location to carry out the experiment
o Same set of microphones for each trial

Method

Measuring the speed of sound with an oscilloscope

 Measuring the speed of sound using an oscilloscope

1. Connect two microphones to an oscilloscope

2. Place them about 2 m apart using a tape measure to measure the distance
between them
3. Set up the oscilloscope so that it triggers when the first microphone detects a
sound, and adjust the time base so that the sound arriving at both microphones
can be seen on the screen
4. Make a large clap using the two wooden blocks next to the first microphone
5. Use the oscilloscope to determine the time at which the clap reaches each
microphone and the time difference between them
6. Repeat this experiment for several distances, e.g. 2 m, 2.5 m, 3 m, 3.5 m

Results

An example results table for obtaining the speed of sound using an oscilloscope

Distance / m Time 1 / s Time 2 / s Time 3 / s Average time / s

2.0
2.5
3.0
3.5
4.0
Analysis of results
Evaluating the experiments

Systematic Errors:

 In experiment 2, ensure the scale of the time base is accounted for correctly
o The scale is likely to be small (e.g. milliseconds) so ensure this is taken
into account when calculating speed

Random errors:

 The main cause of error in experiment 1 is the measurement of time

o Ensure to take repeat readings when timing intervals and calculate an
average to keep this error to a minimum
o Maximise the distance between the two people where possible. This will
reduce the error in measurements of time because the time taken by the
sound waves to travel will be greater

Sound & oscilloscopes

 An oscilloscope is a device that can be used to study a
rapidly changing signal, such as:
o A sound wave
o An alternating current

An oscilloscope is used to display sound as a waveform

Oscilloscopes have lots of dials and buttons, but their main purpose is to display
and measure changing signals like sound waves and alternating current

 When a microphone is connected to an oscilloscope, the (longitudinal) sound

wave is displayed as though it were a transverse wave on the screen
o The properties of longitudinal and transverse waves are explained in the
revision note Transverse & longitudinal waves
  The time base (like the 'x-axis') is used to measure the time period of the wave

An explanation of the sound waveform as displayed on an oscilloscope

A sound wave is displayed as though it were a transverse wave on the screen of

the oscilloscope. The time base can be used to measure a full time period of the
wave cycle

 The height of the wave (measured from the centre of the screen) is related to
the amplitude of the sound

The number of entire waves that appear on the screen is related to

the frequency of the wave

o If the frequency of the sound wave increases, more waves are displayed
on screen

Core practical 7: using an oscilloscope

Aims of the experiment

 The aim of this experiment is to investigate the frequency of a sound wave using
an oscilloscope

Variables

 Independent variable = Tuning forks of different frequencies

 Dependent variable = Time period

Equipment
Equipment Purpose
Tuning fork To generate sound waves of different frequencies
Microphone To detect sound waves from the tuning fork
Oscilloscope To display the sound waves electronically
Wires To connect the microphone to the oscilloscope
Equipment List

Method

A diagram of the oscilloscope and tuning fork set up

Measuring the frequency of a sound wave using an oscilloscope

1. Connect the microphone to the oscilloscope as shown in the image above

2. Test the microphone displays a signal by humming
3. Adjust the time base of the oscilloscope until the signal fits on the screen -
ensure that multiple complete waves can be seen
4. Strike the tuning fork on the edge of a hard surface to generate sound waves of a
pure frequency
5. Hold the tuning fork near to the microphone and observe the sound wave on the
oscilloscope screen
6. Freeze the image on the oscilloscope screen, or take a picture of it
7. Measure and record the time period of the wave signal on the screen by counting
the number of divisions for one complete wave cycle
8. Repeat steps 4-6 for a variety of tuning forks

Results

An example results table of the oscilloscope display

Analysis of results

 To convert the time period of the wave from the number of divisions into
seconds, use the scale of the time base. For example:
o The time base is usually measured in units of ms/cm (milliseconds per
centimetre)
o This would mean a wave with a time base of 4 cm has a time period of 4
ms

 To calculate the frequency of the sound waves produced by the tuning forks, use
the equation:

Evaluating the experiment

Systematic Errors:

 Ensure the scale of the time base is accounted for correctly

o The scale is likely to be small (e.g. milliseconds) so ensure this is taken
into account when calculating the time period

Random Errors:

 A cause of random error in this experiment is noise in the environment, so

ensure it is carried out in a quiet location

Pitch
  The pitch of a sound is related to the frequency of the vibrating source of sound
waves
o If the frequency of vibration is high, the sound wave has a high pitch
o If the frequency of vibration is low, the sound wave has a low pitch

The relationship between the pitch and frequency of sound

The pitch of the sound is related to the frequency of the sound waves

Comparing the pitch of sound displayed on an oscilloscope

This image shows two sound waves displayed on an oscilloscope. The red wave
has smaller wavelength than the blue wave hence it has higher frequency and
higher pitch
Loudness
 The loudness of a sound is related to the amplitude of the vibrating source of
sound waves
 o If the sound is loud, the sound wave has a large amplitude

Comparing the volume of sound displayed on an oscilloscope

This image shows two sound waves displayed on an oscilloscope. The blue wave
has twice the amplitude of the green wave because the blue wave is louder
Range of human hearing
 The human ear responds to the vibrations caused by sound waves
 The frequency range for human hearing is 20 Hz to 20 000 Hz
o Below the frequencies that humans can hear is infrasound
o Above the frequencies that humans can hear is ultrasound

The infrasound, human hearing and ultrasound frequency ranges

The range of human hearing is between 20 – 20 000 Hz. Below 20 Hz is known as

infrasound. Above 20 000 Hz is known as ultrasound
Kinetic theory of gases
Random motion

 Molecules in a gas are in constant random motion at high speeds

 Random motion means that the molecules are travelling in no specific path and
undergo sudden changes in their motion if they collide:
o with the walls of its container
o with other molecules
 The random motion of tiny particles in a fluid is known as Brownian motion

Random motion of gas molecules in a container, caused by collisions

 Brownian motion provides evidence that air is made of small particles

 This is because when larger particles, such as smoke particles or pollen, are
observed floating in the air:
o the larger particles move with random motion
o this is a result of the larger particles colliding with smaller particles that
are invisible to the naked eye

Pressure

 A feature of gases is that they fill their container

 The pressure is defined as the force per unit area

 As the gas particles move about randomly they collide with the walls of their
containers
  These collisions produce a net force at right angles to the wall of the gas
container (or any surface)
 Therefore, a gas at high pressure has more frequent collisions with the
container walls and a greater force
o Hence the higher the pressure, the higher the force exerted per unit area

Gas molecules colliding with the walls of a container, exerting a force over the
area and hence generating pressure
Absolute zero
 The amount of pressure that a gas exerts on its container is dependent on the
temperature of the gas
o This is because particles move with more energy as their temperature
increases
 As the temperature of the gas decreases, the pressure on the container also
decreases
 In 1848, mathematician and physicist, Lord Kelvin, recognised that there must be
a temperature at which the particles in a gas exert no pressure
o At this temperature they must no longer be moving, and hence not
colliding with their container
 This temperature is called absolute zero and is equal to −273 °C
 At absolute zero, or −273 °C, particles will have no net movement. It is therefore
not possible to have a lower temperature

 Absolute zero is defined as:

The temperature at which the molecules in a substance have zero kinetic energy

 This means for a system at absolute zero, it is not possible to remove any more
energy from it
 Even in space, the temperature is roughly 2.7 K above absolute zero

The Kelvin scale

 The Kelvin temperature scale begins at absolute zero
o 0 K is equal to -273 °C
o An increase of 1 K is the same change as an increase of 1 °C
 It is not possible to have a temperature lower than 0 K
 This means a temperature in Kelvin will never be a negative value
 To convert between temperatures θ in the Celsius scale, and T in the Kelvin
scale, use the following conversion:

θ / °C = T / K − 273

T / K = θ / °C + 273
 Conversion chart relating the temperature on the Kelvin and Celsius scales

 The divisions on both scales are equal. This means:

A change in a temperature of 1 K is equal to a change in temperature of 1 °C

Temperature & speed
 Imagine molecules of gas that are free to move around in a box
 The molecules in the gas move around randomly at high speeds, colliding with
surfaces and exerting pressure upon them
 The temperature of a gas is a measure of the average speed of the molecules:
o the higher the temperature of the gas, the faster the molecules move
o This is because they have a greater average speed

Gas molecules move about randomly at high speeds

Temperature & kinetic energy
 Heating a system will change the energy stored in a system by increasing the
kinetic energy of its particles
 o The Kelvin temperature of the gas is related to the average kinetic
energy of the molecules

 This increase in kinetic energy (and therefore energy stored in the system) can:
o Cause the temperature of the system to increase
o Or, produce a change of state (solid to liquid or liquid to gas)

 The internal energy of a gas is the sum of the kinetic energy of all the molecules
 The higher the temperature, the higher the average kinetic energy of the
molecules and vice versa
o This means they move around faster

As the container is heated up, the gas molecules move faster with higher kinetic
energy. The energy stored within the system - the internal energy - therefore
increases

 If the temperature of a gas is increased, the particles move faster and

gain kinetic energy
o Therefore, they will collide more with each other and the container,,
leading to an increase in pressure
 The temperature (in Kelvin) is proportional to the average kinetic energy of the
molecules

T ∝ KE
The Gas laws
 Gas laws provide explanations for the relationships between:
o Pressure and volume at a constant temperature
o Pressure and (kelvin) temperature at a constant volume
Pressure & volume

 If the temperature of a gas remains constant, the pressure of the gas changes
when it is:
o compressed – decreases the volume which increases the pressure
o expanded – increases the volume which decreases the pressure

Pressure increases when a gas is compressed

 Similarly, a change in pressure can cause a change in volume

 A vacuum pump can be used to remove the air from a sealed container
 The diagram below shows the change in volume to a tied up balloon when the
pressure of the air around it decreases:

By changing the pressure around the balloon, its change in volume can be seen

 For a fixed temperature, if the gas is compressed, the pressure will increase
o The particles travel the same speed as before, but the distance they travel
is reduced when the container is smaller
 o The molecules will hit the walls of the container more frequently
o This creates a larger overall net force on the walls which increases
the pressure

Pressure & temperature

 The motion of molecules in a gas changes according to the temperature

 As the temperature of a gas increases, the average speed of the molecules
also increases
 Since the average kinetic energy depends on their speed, the kinetic energy of
the molecules also increases if its volume remains constant
o The hotter the gas, the higher the average kinetic energy
o The cooler the gas, the lower the average kinetic energy

 If the gas is heated up, the molecules will travel at a higher speed
o This means they will collide with the walls more often
o This creates an increase in pressure

 Therefore, at a constant volume, an increase in temperature increases the

pressure of a gas and vice versa
 Diagram A shows molecules in the same volume collide with the walls of the
container more with an increase in temperature
 Diagram B shows that since the temperature is proportional to the pressure, the
graph against each is a straight line
 At constant volume, an increase in the temperature of the gas increases the
pressure due to more collisions on the container walls
The pressure law
 If the volume V of an ideal gas is constant, the pressure law is given by:

P∝T

 This means the pressure is proportional to the temperature

Pressure and temperature are proportional. Doubling temperature also doubles
the pressure for a gas in a fixed volume.

 The relationship between the pressure and (Kelvin) temperature for a fixed mass
of gas at constant volume can also be written as:

Pressure law graph representing temperature (in °C) directly proportional to the
volume
Boyle's law
 For a fixed mass of a gas held at a constant temperature, the Boyle's law formula
is:

pV = constant

 Where:
o p = pressure in pascals (Pa)
o V = volume in metres cubed (m3)

 This means that the pressure and volume are inversely proportional to each
other
o When the volume decreases (compression), the pressure increases
o When the volume increases (expansion), the pressure decreases
 This is because when the volume decreases, the same number of particles
collide with the walls of a container but more frequently as there is less space
o However, the particles still collide with the same amount of force meaning
greater force per unit area (pressure)
 The key assumption is that the temperature and the mass (and number) of the
particles remains the same

Increasing the volume of a gas decreases its pressure

 This equation can also be rewritten for comparing the pressure and volume
before and after a change in a gas:

p 1V1 = p 2V2

 Where:
o p1 = initial pressure in pascals (Pa)
o V1 = initial volume in metres cubed (m3)
o p2 = final pressure in pascals (Pa)
o V2 = final volume in metres cubed (m3)

 This equation is sometimes referred to as Boyle's Law

 Initial pressure and volume, p1 and V1, and final pressure and volume, p2 and V2.
When volume decreases, pressure increases
The law of magnetism
Poles of a magnet

 The ends of a magnet are called poles

 Magnets have two poles: a north and a south

Poles of a Magnet

The law of magnetism

 When two magnets are held close together, there will be an attractive or
repulsive force between the magnets depending on how they are arranged:

Opposite poles attract; like poles repel

 The law of magnetism states that:

o Two like poles repel (e.g. S and S or N and N)
o Two opposite poles attract (e.g. S and N)
 The attraction or repulsion between two magnetic poles occurs due to
the magnetic force

Magnetic materials
 Magnetic materials can be soft or hard
 Magnetically soft materials (e.g. iron):
o Are easy to magnetise
o Easily lose their magnetism (temporarily magnetised)
 Magnetically hard materials (e.g. steel):
o Are difficult to magnetise
o Do not easily lose their magnetism (permanently magnetised)
 Permanent magnets are made out of magnetically hard materials
  Electromagnets are made out of magnetically soft materials
o This means that electromagnets can be made magnetic or non-magnetic
as an when required

A steel pin will be attracted when an electromagnet switches on but not when it
switches off. It is always attracted to a permanent magnet
Magnetic field lines
 All magnets are surrounded by a magnetic field
 A magnetic field is defined as:

The region around a magnet where a force acts on another magnet or on a

magnetic material (such as iron, steel, cobalt and nickel)

Magnetic field lines

 Magnetic field lines are used to represent the strength and direction of a
magnetic field
 The direction of the magnetic field is shown using arrows
 The strength of the magnetic field is shown by the spacing of the magnetic field
lines
o If the magnetic field lines are close together then the magnetic field will
be strong
o If the magnetic field lines are far apart then the magnetic field will
be weak
 There are some rules which must be followed when drawing magnetic field lines.
Magnetic field lines:
o Always go from north to south (indicated by an arrow midway along the
line)
o two magnetic field lines must never touch or cross other field lines

Magnetic field around a bar magnet

 The magnetic field is strongest at the poles
o This is where the magnetic field lines are closest together
 The magnetic field becomes weaker as the distance from the magnet
increases
 This is shown by the magnetic field lines are getting further apart

The magnetic field around a bar magnet

 Two bar magnets can repel or attract, the field lines will look slightly different for
each:

Magnetic field lines for attracting and repelling bar magnets

 Therefore, the magnetic field lines around different configurations of two bar
magnets would look like:
 Magnetic field lines between two bar magnets
Representing magnetic fields
 Two bar magnets can be used to produce a uniform magnetic field
 Point opposite poles (north and south) of the two magnets a few centimetres
apart
 A uniform magnetic field will be produced in the gaps between opposite poles
o Note: Outside that gap, the field will not be uniform

A uniform field is created when two opposite poles are held close together.
Magnetic fields are always directed from North to South. Note that the rest of
each magnet is not shown, but the magnet with a north pole also has a south
pole not shown and vice versa for the south pole shown above.

 A uniform magnetic field is one that has the same strength and direction at all
points
o To show that the magnetic field has the same strength at all points there
must be equal spacing between all magnetic field lines
o To show that the magnetic field is acting in the same direction at all points
there must be an arrow on each magnetic field line going from
the north pole to the south pole

 The magnetic field lines are the same distance apart between the gaps of the
poles to indicate that the field strength is the same at every point between the
poles
Permanent & induced magnets
Magnetic materials

Magnetic materials are attracted to a magnet; non-magnetic materials are not

 Magnetic materials are materials which are attracted by magnets

o Being a magnetic material does not mean the material is itself a magnet
 Very few metals in the periodic table are magnetic, these include:
o Iron
o Cobalt
o Nickel
 Steel is an alloy which contains iron, so it is also magnetic
 Magnetic materials will always be attracted to the magnet, regardless of which
pole is held close to it

Magnetic materials attracted to either pole of a magnet

 To test whether a material is a magnet it should be brought close to a known

magnet
o If it can be repelled by the known magnet then the material itself is a
magnet
o If it can only be attracted and not repelled then it is a magnetic material

 There are two types of magnets

 Permanent magnets
 Induced magnets

Permanent magnets
  Permanent magnets are made out of permanent magnetic materials, for example
steel
 A permanent magnet will produce its own magnetic field
o It will not lose its magnetism

Induced magnets

 When a magnetic material is placed in a magnetic field, the material can

temporarily be turned into a magnet.
o This is called induced magnetism
 When magnetism is induced in a material:
o One end of the material will become a north pole
o The other end will become a south pole
 Magnetic materials will always be attracted to a permanent magnet
o This means that the end of the material closest to the magnet will have
the opposite pole to magnets pole closest to the material

Inducing magnetism in a magnetic material

 When the magnetic material is removed from the magnetic field it will lose
most/all of its magnetism quickly

Core practical 12: investigating magnetic fields

Aim of the experiment

 To investigate the magnetic field pattern for a permanent bar magnet and
between two bar magnets

Equipment

Equipment List
 Equipment Purpose
Two bar magnets Produce a magnetic field which is plotted
Plotting compasses Show the direction of the magnetic field at a given point
Paper Plot the magnetic field pattern on this
Pencil Plot the magnetic field pattern with this
Method

Step 1:

 Place the magnet on top of a piece of paper

 Draw a dot at one end of the magnet (near its corner)

Step 2:

 Place a plotting compass next to the dot, so that one end of the needle of the
compass points away from the dot
 Use a pencil to draw a new dot at the other side of the compass needle

Step 3:

 Move the compass so that it points away from the new dot, and repeat the
process above
Step 4:

 Keep repeating the previous process until there is a chain of dots going from one
end of the magnet to the other
 Then remove the compass, and link the dots using a smooth curve – this will be
the magnetic field line

Step 5:

 Repeat the whole process several times to create several other magnetic field
lines
Step 6:

 Repeat the whole process for two bar magnets placed 5 cm apart first facing the
same pole then facing opposite poles

Analysis of results

 The magnetic field pattern for the single bar magnetic should look like this:

The magnetic field of a bar magnet plotted

 The magnetic field pattern for two bar magnets should look like this:

Magnetic field of two bar magnets interacting

Evaluating the experiment

 Make sure the pencil you use is sharp to provide a clear and accurate drawing of
the field lines
 Read the marker on the compass from above and not at an angle
 Allow the compasses to settle for a couple of seconds before taking the reading

Electromagnetism
Magnetic field of a wire carrying current

 When a current flows through a conducting wire a magnetic field is produced

around the wire
 The shape and direction of the magnetic field can be investigated using plotting
compasses

Diagram showing the magnetic field around a current-carrying wire

 The magnetic field is made up of concentric circles

o A circular field pattern indicates that the magnetic field around a current-
carrying wire has no poles
 As the distance from the wire increases the circles get further apart
o This shows that the magnetic field is strongest closest to the wire and gets
weaker as the distance from the wire increases
 The right-hand thumb rule can be used to work out the direction of the
magnetic field
The right-hand thumb rule shows the direction of current flow through a wire and
the direction of the magnetic field around the wire

 Reversing the direction in which the current flows through the wire will reverse
the direction of the magnetic field

Side and top view of the current flowing through a wire and the magnetic field
produced
  If there is no current flowing through the conductor there will be no magnetic
field
 Increasing the amount of current flowing through the wire will increase the
strength of the magnetic field
o This means the field lines will become closer together

Factors affecting field strength

 The strength of the magnetic fields field depends on:

o The size of the current
o The distance from the long straight conductor (such as a wire)
 A larger current will produce a larger magnetic field and vice versa
 The greater the distance from the conductor, the weaker the magnetic
field and vice versa

The greater the current, the stronger the magnetic field. This is shown by more
concentrated field lines
Magnetic force on a current-carrying wire
 The motor effect occurs when:

A wire with current flowing through it is placed in a magnetic field and

experiences a force

 This effect is a result of two interacting magnetic fields

o One is produced around the wire due to the current flowing through it
o The second is the magnetic field into which the wire is placed, for
example, between two magnets

 As a result of the interactions of the two magnetic fields, the wire will experience
a force
  When no current is passed through a conductor in a magnetic field, however, it
will experience no force

The motor effect is a result of two magnetic fields interacting to produce a force
on the wire

The D.C. motor

 The motor effect can be used to create a simple d.c. electric motor
o The force on a current-carrying coil is used to make it rotate in a single
direction

 The simple D.C. motor consists of a coil of wire (which is free to rotate)
positioned in a uniform magnetic field
 The coil of wire, when horizontal, forms a complete circuit with a cell
o The coil is attached to a split ring (a circular tube of metal split in two)
o This split ring is connected in a circuit with the cell via contact with
conducting carbon brushes

Forces on the horizontal coil in a D.C. motor

Forces acting in opposite directions on each side of the coil, causing it to rotate.
The split ring connects the coil to the flow of current

 Current flowing through the coil produces a magnetic field

o This magnetic field interacts with the uniform external field, so a force is
exerted on the wire
 Forces act in opposite directions on each side of the coil, causing it to rotate:
o On the blue side of the coil, current travels towards the cell so the force
acts upwards (using Fleming's left-hand rule)
o On the black side, current flows away from the cell so the force acts
downwards
 Once the coil has rotated 90°, the split ring is no longer in contact with the
brushes
o No current flows through the coil so no forces act

Coil in the vertical position

No force acts on the coil when vertical, as the split ring is not in contact with the
brushes

 Even though no force acts, the momentum of the coil causes the coil to continue
to rotate slightly
 The split ring reconnects with the carbon brushes and current flows through the
coil again
o Now the blue side is on the right and the black side is on the left
 Current still flows toward the cell on the left and away from the cell on the right,
even though the coil has flipped
o The black side of the coil experiences an upward force on the left and the
blue side experiences a downward force on the right
o The coil continues to rotate in the same direction, forming a continuously
spinning motor

Forces on the coil when rotated 180°

Even though the coil has flipped, current still flows anticlockwise and the forces
still cause rotation in the same direction

Factors affecting the D.C. motor

 The speed at which the coil rotates can be increased by:

o Increasing the current
o Increasing the strength of the magnetic field
 The direction of rotation of coil in the D.C. motor can be changed by:
o Reversing the direction of the current
o Reversing the direction of the magnetic field by reversing the poles of the
magnet
 The force supplied by the motor can be increased by:
o Increasing the current in the coil
o Increasing the strength of the magnetic field
o Adding more turns to the coil
Loudspeakers

 Loudspeakers and headphones convert electrical signals into sound

o They work due to the motor effect
 They work in the opposite way to microphones
 A loudspeaker consists of a coil of wire which is wrapped around one pole of
a permanent magnet

Diagram showing a cross-section of a loudspeaker

 An alternating current passes through the coil of the loudspeaker

o This creates a changing magnetic field around the coil
 As the current is constantly changing direction, the direction of the magnetic field
will be constantly changing
 The magnetic field produced around the coil interacts with the field from the
permanent magnet
 The interacting magnetic fields will exert a force on the coil
o The direction of the force at any instant can be determined
using Fleming’s left-hand rule

 As the magnetic field is constantly changing direction, the force exerted on the
coil will constantly change direction
o This makes the coil oscillate
 The oscillating coil causes the speaker cone to oscillate
o This makes the air oscillate, creating sound waves

Factors affecting magnetic force

 Magnetic forces are due to interactions between magnetic fields
o Stronger magnetic fields produce stronger forces and vice versa
 For a current carrying conductor, the size of the force exerted by the magnetic
fields can be increased by:
 o Increasing the amount of current flowing through the wire
 This will increase the magnetic field around the wire
o Using stronger magnets
 This will increase the magnetic field between the poles of the
magnet
o Placing the wire at 90o to the direction of the magnetic field lines between
the poles of the magnet
 This will result in the maximum interaction between the two
magnetic fields

 Note: If the two magnetic fields are parallel there will be no interaction between
the two magnetic fields and therefore no force produced

Fleming's left-hand rule

 The direction of the force (aka the thrust) on a current-carrying wire depends
on the direction of
o the current
o the magnetic field
 All three will be perpendicular to each other in Fleming's left-hand rule questions
o This means that sometimes the force could be into and out of the page (in
3D)

 The direction of the force (or thrust) can be worked out by using Fleming's left-
hand rule:

Fleming’s left-hand rule can be used to determine the directions of the force,
magnetic field and current
Electromagnets
 When an electric current flows in a wire it creates a magnetic field around the
wire
  By winding the wire into a coil we can strengthen the magnetic field by
concentrating the field lines
 If this wire is wound around a soft magnet, such as an iron, then an
electromagnet is made (see the electromagnet diagram below)
o The electromagnet is magnetic only when current flows through the wire

Electromagnet diagram

Electromagnets are made up of a coil of wire wrapped around an iron core

 The strength of an electromagnet’s magnetic field may be increased by:

o Increasing the current in the coil
o Adding more turns to the coil

 The magnetic field around an electromagnet has the same shape as the one
around a bar magnet
 The field can be reversed by reversing the direction of the current
o However, bar magnets are always magnetic, unlike electromagnets

Magnetic field patterns

 Magnetic field line patterns are all slightly different around:
o Straight wires
o Flat circular coils
o Solenoids

Magnetic field in a straight wire

 When a current flows through a conducting wire a magnetic field is produced

around the wire
 The shape and direction of the magnetic field can be investigated using plotting
compasses

 The magnetic field is made up of concentric circles

 o A circular field pattern indicates that the magnetic field around a current-
carrying wire has no poles
 As the distance from the wire increases the circles get further apart
o This shows that the magnetic field is strongest closest to the wire and gets
weaker as the distance from the wire increases
 The right-hand thumb rule can be used to work out the direction of the
magnetic field

The direction of the magnetic field around a wire is given by the right-hand thumb
rule

 Reversing the direction in which the current flows through the wire will reverse
the direction of the magnetic field
 If there is no current flowing through the conductor there will be no magnetic
field
 Increasing the amount of current flowing through the wire will increase the
strength of the magnetic field
o This means the field lines will become closer together

Magnetic field in a flat circular coil

 When a wire is looped into a coil, the magnetic field lines circle around each part
of the coil, passing through the centre of it
 The magnetic field around a flat circular coil

 To increase the strength of the magnetic field around the wire it should be coiled
to form a solenoid
 The magnetic field around the solenoid is similar to that of a bar magnet
 Using this, we can draw the pattern of magnetic field lines of a current carrying
solenoid

Magnetic field around and through a solenoid. This is similar to the field of a bar
magnet.

Magnetic field in a solenoid

 The magnetic field inside the solenoid is strong and uniform

 Inside a solenoid (an example of an electromagnet) the fields from individual
coils
o Add together to form a very strong almost uniform field along
the centre of the solenoid
o Cancel to give a weaker field outside the solenoid
  One end of the solenoid behaves like the north pole of a magnet; the other side
behaves like the south pole
o To work out the polarity of each end of the solenoid it needs to be viewed
from the end
o If the current is travelling around in a clockwise direction then it is
the south pole
o If the current is travelling around in an anticlockwise direction then it is
the north pole
 If the current changes direction then the north and south poles will be
reversed
 If there is no current flowing through the wire then there will be no magnetic
field produced around or through the solenoid

Poles of a solenoid. The right hand rule can be adapted for this situation, with
fingers following the direction of current and the thumb pointing in the direction
of the central magnetic field lines.

Factors affecting magnetic field strength of a solenoid

 The strength of the magnetic field produced around a solenoid can be increased
by:
o Increasing the size of the current which is flowing through the wire
o Increasing the number of coils
o Adding an iron core through the centre of the coils

 The iron core will become an induced magnet when current is flowing through
the coils
 The magnetic field produced from the solenoid and the iron core will create a
much stronger magnet overall

Magnetic force on a charge

 When a current-carrying wire is placed in a magnetic field, it will experience a
force if the wire is perpendicular
 o This is because the magnetic field exerts a force on each individual
electron flowing through the wire

 Therefore, when a charged particle passes through a magnetic field, the field can
exert a force on the particle, causing it to deflect

o The force is always at 90 degrees to both the direction of travel and the
magnetic field lines

o The direction can be worked out by using Fleming's left-hand rule

The electron experiences a force upwards when it travels through the magnetic
field between the two poles. Remember that conventional current flows in the
opposite direction to electrons.

 If the particle is travelling perpendicular to the field lines:

o It will experience the maximum force

 If the particle is travelling parallel to the field lines:

o It will experience no force

 If the particle is travelling at an angle to the field lines:

o It will experience a small force

Electromagnetic induction
 Electromagnetic (EM) induction is used to generate electricity
 EM induction is when:

A voltage is induced in a conductor or a coil when it moves through a magnetic

field or when a magnetic field changes through it

 This is done by the conductor or coil cutting through the magnetic field lines of
the magnetic field
 This is often referred to as the generator effect and is the opposite to the motor
effect
o In the motor effect, there is already a current in the conductor which
experiences a force
o In the generator effect, there is no initial current in the conductor but one
is induced (created) when it moves through a magnetic field
  This is done by the conductor or coil cutting through the magnetic field lines of
the magnetic field

Generating potential difference

 A potential difference will be induced in the conductor if there is relative

movement between the conductor and the magnetic field
 Moving the electrical conductor in a fixed magnetic field
o When a conductor (such as a wire) is moved through a magnetic field, the
wire cuts through the fields lines
o This induces a potential difference in the wire

Electromagnetic induction diagram

Moving an electrical conductor in a magnetic field to induce a potential difference

 Moving the magnetic field relative to a fixed conductor

o As the magnet moved through the coil, the field lines cut through the turns
on the coil
o This induces a potential difference in the coil

Diagram of electromagnetic induction in a coil

When the magnet enters the coil, the field lines cut through the turns, inducing a
potential difference

 A sensitive voltmeter can be used to measure the size of the induced potential
difference
 If the conductor is part of a complete circuit then a current is induced in the
conductor

Factors affecting the induced potential difference

 The size of the induced potential difference is determined by:

o The speed at which the wire, coil or magnet is moved
o The number of turns on the coils of wire
o The size of the coils
o The strength of the magnetic field

 The direction of the induced potential difference is determined by:

o The orientation of the poles of the magnet

1. The speed at which the wire, coil or magnet is moved:

 Increasing the speed will increase the rate at which the magnetic field lines are
cut
 This will increase the induced potential difference

2. The number of turns on the coils in the wire:

 Increasing the number of turns on the coils in the wire will increase the
potential difference induced
 This is because each coil will cut through the magnetic field lines and the total
potential difference induced will be the result of all of the coils cutting the
magnetic field lines

3. The size of the coils:

 Increasing the area of the coils will increase the potential difference induced
 This is because there will be more wire to cut through the magnetic field lines

4. The strength of the magnetic field:

 Increasing the strength of the magnetic field will increase the potential
difference induced

5. The orientation of the poles of the magnet:

 Reversing the direction in which the wire, coil or magnet is moved

Generators & dynamos
 The generator effect can be used to:
o Generate a.c in an generator
o Generate d.c in a dynamo

Alternator

 A simple alternator is a type of generator that converts mechanical energy to

electrical energy in the form of alternating current

An alternator is a rotating coil in a magnetic field with slip rings

 A rectangular coil that is forced to spin in a uniform magnetic field

 The coil is connected to a centre-reading meter by metal brushes that press on
two metal slip rings
o The slip rings and brushes provide a continuous connection between the
coil and the meter
 When the coil turns in one direction:
o The pointer deflects first one way, then the opposite way, and then back
again
o This is because the coil cuts through the magnetic field lines and an
alternating potential difference, and therefore current, is induced in the
coil
 An alternating current may also be produced when a magnet rotates within a
stationary coil
o Both methods operate on the principle that p.d. is induced when a coil
experiences a changing external magnetic field
  The induced potential difference and the current alternate because they
repeatedly change direction

a.c output from an alternator - the current is both in the positive and negative
region of the graph

Dynamos

 A dynamo in physics is the name for a a direct current generator

 A simple dynamo is the same as an alternator except that the dynamo has
a split-ring commutator instead of two separate slip rings

A dynamo is a rotating coil in a magnetic field connected to a split ring

commutator
  As the coil rotates, it cuts through the field lines
o This induces a potential difference between the end of the coil
 The split ring commutator changes the connections between the coil and the
brushes every half turn in order to keep the current leaving the dynamo in
the same direction
o This happens each time the coil is perpendicular to the magnetic field lines

 Therefore, the induced potential difference does not reverse its direction as it
does in the alternator
 Instead, it varies from zero to a maximum value twice each cycle of rotation, and
never changes polarity (positive to negative)
o This means the current is always positive (or always negative)

D.C output from a dynamo - the current is only in the positive region of the graph
Transformers
 A transformer is a device used to change the value of an alternating potential
difference or current
 This is achieved using the generator effect

Structure of a transformer

 A basic transformer consists of:

o A primary coil
o A secondary coil
o An iron core

 Iron is used because it is easily magnetised

 Structure of a transformer

How a transformer works

 An alternating current is supplied to the primary coil

 The current is continually changing direction
o This means it will produce a changing magnetic field around the primary
coil

 The iron core is easily magnetised, so the changing magnetic field passes
through it
 As a result, there is now a changing magnetic field inside the secondary coil
o This changing field cuts through the secondary coil and induces a
potential difference

 As the magnetic field is continually changing the potential difference induced will
be alternating
o The alternating potential difference will have the same frequency as the
alternating current supplied to the primary coil
 If the secondary coil is part of a complete circuit it will cause an alternating
current to flow

Step-up & step-down Transformers

 A transformer can change the size of an alternating voltage
 They also have a number of other roles, such as:
o To increase the potential difference of electricity before it is transmitted
across the national grid
o To lower the high voltage electricity used in power lines to the lower
voltages used in houses
o Used in adapters to lower mains voltage to the lower voltages used by
many electronic devices

 A step-up transformer increases the potential difference of a power source.

 o A step-up transformer has more turns on the secondary coil than on the
primary coil
 A step-down transformer decreases the potential difference of a power
source.
o A step-down transformer has fewer turns on the secondary coil than on
the primary coil

Transformers in electricity transmission

What does a step up transformer do?

 When electricity is transmitted over large distances, the current in the

wires heats them, resulting in energy loss
 The electrical energy is transferred at high voltages from power stations
 It is then transferred at lower voltages in each locality for domestic uses
 The voltage must be stepped up by a step-up transformer
o These are placed after the power station

Why are step down transformers used?

 For the domestic use of electricity, the voltage must be much lower
 This is done by stepping down by the voltage using a step-down transformer
o These are placed before buildings

Electricity is transmitted at high voltage, reducing the current and hence power
loss in the cables using transformers
Step-up transformer

 A step-up transformer increases the potential difference of a power source

 A step-up transformer has more turns on the secondary coil than on the
primary coil (Ns > Np)

Step-down transformer

 A step-down transformer decreases the potential difference of a power source

 A step-down transformer has fewer turns on the secondary coil than on the
primary coil (Ns < Np)

Atomic structure
  Atoms are the building blocks of all matter
 They are incredibly small, with a radius of only 1 × 10-10 m
o This means that about one hundred million atoms could fit side by side
across your thumbnail

 Atoms have a tiny, dense nucleus at their centre, with electrons orbiting around
the nucleus
 The radius of the nucleus is over 10,000 times smaller than the whole atom, but it
contains almost all of the mass of the atom

Atomic structure of lithium

Diagram showing the structure of a Lithium atom. If drawn to scale then the
electrons would be around 100 metres away from the nucleus!

Particles in the atom

 The nucleus contains:

o Protons - positively charged particles with a relative atomic mass of one
unit
o Neutrons – no charge, and also with a relative atomic mass of one unit

 Almost all of the atom is empty space, but moving around the nucleus there are:
o Electrons – negative charge with almost no mass (1/2000 the mass of a
proton or neutron)

 The properties of each of the particles are shown in the table below:

Table of particle properties

Particle Location Relative charge Relative mass

proton in the nucleus +1 1
neutron in the nucleus 0 1
electron orbiting the nucleus −1 1/2000 (negligible)
Charge in the atom
  Although atoms contain particles of different charge, the total charge within an
atom is zero
o This is because the number of electrons is equal to the number
of protons
 The following table sets out the calculation of the total charge in the lithium atom
in the diagram above:

Calculating total charge table

Particle Relative charge Number of particles in lithium atom number × relative charge Total charge
proton +1 3 +3
neutron 0 4 0 (+3) + 0 + (−3) = 0
electron −1 3 −3
 If an atom loses electrons, then it is said to be ionised
 Symbols are used to describe particular nuclear by their element symbol, atomic
number and mass number
o This notation is called nuclear notation

Carbon 12 in nuclear notation

Atomic & mass number
Atomic number

 The number of protons in an atom is called its atomic number (it can also be
called the proton number)
o Elements in the periodic table are ordered by their atomic number
o Therefore, the number of protons determines which element an atom is

 The atomic number of a particular element is always the same

 For example:
o Hydrogen has an atomic number of 1. It always has just one proton
o Sodium has an atomic number of 11. It has 11 protons
o Uranium has an atomic number of 92. It has 92 protons

 The atomic number is also equal to the number of electrons in an atom

o This is because atoms have the same number of electrons and protons in
order to have no overall charge

Mass number
  The total number of particles in the nucleus of an atom is called its mass
number (it can also be called the nucleon number)
 The mass number is the number of protons and neutrons in the atom
 The number of neutrons can be found by subtracting the atomic number from
the mass number

number of neutrons = mass number – atomic number

 For example, if a sodium atom has a mass number of 23 and an atomic number
of 11, then the number of neutrons would be 23 – 11 = 12

Nuclear notation

 The mass number and atomic number of an atom are shown by writing them with
the atomic symbol
o This is called nuclear notation

 Here are three examples:

Examples of nuclear notation for atoms of Hydrogen, Sodium and Uranium

 The top number is the mass number

o This is equal to the total number of particles (protons and neutrons) in the
nucleus

 The lower number is the atomic number

o This is equal to the total number of protons in the nucleus
 The atomic and mass number of each type of atom in the examples above is
shown in this table:

Number of protons, neutrons & electrons table

Number of protons Number of neutrons Number of electrons

Atom
(atomic number) (mass number − atomic number) (same as atomic number)
hydrogen 1 1 1
sodium 11 12 11
uranium 92 143 92
Isotopes
 For a particular element, the number of protons is always the same, but the
number of neutrons can be different
o This is because the number of protons determines the element e.g.
carbon atoms have 6 protons and iron atoms have 26 protons

 An isotope is defined as:

An atom, or atoms, of the same element that have an equal number of protons but
a different number of neutrons

 Each element can have more than one isotope

Isotopes of hydrogen

 Some isotopes are more unstable than others due to the imbalance of protons
and neutrons, which means
o They may be more likely to decay
o They may be less likely to occur naturally

 For example, about 2 in every 10 000 atoms of hydrogen are the isotope
deuterium
o The isotope tritium is even rarer (about 1 in every billion billion atoms of
hydrogen)
Types of radiation
 Some atomic nuclei are unstable and radioactive
 This is because of an imbalance of protons or neutrons in the nucleus
 Carbon-14 is an example of an isotope of carbon which is unstable
 This is because it has two extra neutrons compared to a stable nucleus of
carbon-12

Stable and unstable isotopes of carbon

Carbon-12 is stable, whereas carbon-14 is unstable because it has two extra

neutrons

 Unstable nuclei can emit radiation to become more stable

 Radiation can be in the form of a high-energy particle or wave
 This process is known as radioactive decay

 As the radiation moves away from the nucleus, it takes some energy with it
 This makes the nucleus more stable

Radioactive decay of a nucleus

Unstable nuclei decay by emitting high energy particles or waves

 When an unstable nucleus decays, it emits radiation

  The different types of radiation that can be emitted are:
o Alpha (α) particles
o Beta (β-) particles
o Gamma (γ) radiation

 These changes are spontaneous and random

Properties of radiation
Alpha particles

 The symbol for alpha is α

 An alpha particle is the same as a helium nucleus
 This is because it consists of two neutrons and two protons

Beta particles

 The symbol for beta is β−

 Beta particles are high-energy electrons
 They are produced in nuclei when a neutron changes into a proton and an
electron

Gamma rays

 The symbol for gamma is γ

 Gamma rays are electromagnetic waves
 They have the highest energy of the different types of electromagnetic waves

Alpha, beta & gamma radiation

Alpha particles, beta particles and gamma waves can be emitted from unstable
nuclei
 Properties of alpha, beta & gamma

 Alpha (α), beta (β) and gamma (γ) radiation can be identified by their:
o Nature (what type of particle or radiation they are)
o Ionising ability (how easily they ionise other atoms)
o Penetrating power (how far can they travel before they are stopped
completely)

 Alpha, beta and gamma penetrate materials in different ways

 This means they are stopped, or reduced, by different materials

Penetrating power of alpha, beta and gamma

Alpha, beta and gamma are different in how they penetrate materials. Alpha is the
least penetrating, and gamma is the most penetrating

 Alpha is stopped by paper, whereas beta and gamma pass through it

 Beta is stopped by a few millimetres of aluminium
 Gamma rays can pass through aluminium but are only partially stopped by
thick lead

Summary of the properties of nuclear radiation

Ionising
Particle Nature Range in air Penetrating power
ability
helium nucleus (2 protons, 2
Alpha (α) a few cm low; stopped by a thin sheet of paper high
neutrons)
a few 10s of moderate; stopped by a few mm of aluminium
Beta (β) high-energy electron moderate
cm foil or Perspex
Gamma
electromagnetic wave infinite high; reduced by a few cm of lead low
(γ)
Core practical 13: investigating radiation
 Aim of the experiment

 The aim of this experiment is to investigate the penetration powers of different

types of radiation using either radioactive sources or simulations

Variables:

 Independent variable = Absorber material

 Dependent variable = Count rate
 Control variables:
o Radioactive source
o Distance of GM tube to source
o Location / background radiation

Equipment List

Equipment Purpose
radioactive sources (α, β and γ) to use as a source of radioactive emission
ruler to measure the distance between the source and detector
mount for radioactive source to secure the source in place
Geiger-Muller tube and counter to measure the count rate of a radioactive source
tongs to safely handle the sources at a distance
selection of absorbing materials (paper, aluminium foil, to place between the source and detector to investigate effect on
lead) count rate
lead-lined containers for radioactive sources to store sources in when not in use

 Resolution of measuring equipment:

o Ruler = 1 mm
o Geiger-Müller tube = 0.01 μS/hr

Method
Apparatus for investigating the penetrating powers of different types of radiation

1. Connect the Geiger-Müller tube to the counter and, without any sources present,
measure background radiation over a period of one minute
2. Repeat this three times, and take an average. Subtract this value from all
subsequent readings.
3. Place a radioactive source a fixed distance of 3 cm away from the tube and take
another reading of count rate over a period of one minute
4. Take a set of absorbers, i.e. some paper, several different thicknesses of
aluminium (increasing in 0.5 mm intervals) and different thicknesses of lead
5. One at a time, place these absorbers between the source and the tube and take
another reading of count rate over a period of one minute
6. Repeat the above experiment for other radioactive sources

Analysis of results

 If the count rate is similar to background levels (allowing for a little random
variation), then the radiation has all been absorbed
o Note: some sources will emit more than one type of radiation

 If the count rate reduces when paper is present, the source is emitting alpha
 If the count rate reduces when a few mm of aluminium is present, then the
source is emitting beta
 If some radiation is still able to penetrate a few mm of lead, then the source is
emitting gamma
 Penetrating power of alpha, beta and gamma radiation

Evaluating the experiment

Systematic Errors:

 Make sure that the sources are stored well away from the counter during the
experiment
 Conduct all runs of the experiment in the same location to avoid changes in
background radiation levels

Random Errors:

 The accuracy of such an experiment is improved with using reliable sources with
a long half-life and an activity well above the natural background level

Safety considerations

 When not using a source, keep it in a lead-lined container

 When in use, try and keep a good distance (a metre or so) between yourself and
the source
 When handling the source, do so using tweezers (or tongs) and point the source
away from you

Alpha, beta, gamma & neutron emission

Alpha decay

 During alpha decay, an alpha particle is emitted from an unstable nucleus

 A completely new element is formed in the process
Alpha decay usually happens in large unstable nuclei, causing the overall mass
and charge of the nucleus to decrease

 An alpha particle is a helium nucleus

o It is made of 2 protons and 2 neutrons

 When the alpha particle is emitted from the unstable nucleus, the mass number
and atomic number of the nucleus changes
o The mass number decreases by 4
o The atomic number decreases by 2
 Alpha decay can be represented by the following nuclear equation:

Beta decay

 During beta decay, a neutron changes into a proton and an electron

o The electron is emitted and the proton remains in the nuclei
 A completely new element is formed because the atomic number changes
 Beta decay often happens in unstable nuclei that have too many neutrons. The
mass number stays the same, but the atomic number increases by one

 A beta particle is a high-speed electron

 It has a mass number of 0
o This is because the electron has a negligible mass, compared to neutrons
and protons
 Therefore, the mass number of the decaying nuclei remains the same
 Electrons have an atomic number of -1
o This means that the atomic number of the new nucleus will increase by
1 to balance the overall atomic number before and after the decay

Gamma decay

 During gamma decay, a gamma ray is emitted from an unstable nucleus

 The process that makes the nucleus less energetic but does not change its
structure

Gamma decay does not affect the mass number or the atomic number of the
radioactive nucleus, but it does reduce the energy of the nucleus
  The gamma ray that is emitted has a lot of energy, but no mass or charge
 Gamma decay can be represented by the following nuclear equation:

Neutron emission

 A small number of isotopes can decay by emitting neutrons

 When a nucleus emits a neutron:
o The atomic number (number of protons) does not change
o The mass number (total number of nucleons) decreases by 1

 Neutron emission can be represented by the following nuclear equation:

Decay equations
 Radioactive decay events can be shown using nuclear decay equations
 A decay equation is similar to a chemical reaction equation as
o the particles present before the decay are shown before the arrow
o the particles produced in the decay are shown after the arrow

 In a decay equation:
o the sum of the mass numbers before and after the reaction must be
the same
 o the sum of the atomic numbers before and after the reaction must be
the same

 The following decay equation shows polonium-212 undergoing alpha decay

Detecting radiation
 Ionising radiation can be detected using
o photographic film
o a Geiger–Müller tube

Photographic film

 Photographic films detect radiation by becoming darker when it absorbs

radiation, similar to when it absorbs visible light
o The more radiation the film absorbs, the darker it is when it is developed

 People who work with radiation, such as radiographers, wear film badges which
are checked regularly to monitor the levels of radiation absorbed
 To get an accurate measure of the dose received, the badge contains different
materials that the radiation must penetrate to reach the film
o These materials may include aluminium, copper, paper, lead and plastic

 The diagram shows what a typical radiation badge looks like:

A badge containing photographic film can be used to monitor a person’s

exposure to radiation
Geiger-Müller tube

 The Geiger-Müller tube is the most common device used to measure and detect
radiation
 Each time it absorbs radiation, it transmits an electrical pulse to a counting
machine
 This makes a clicking sound or displays the count rate
 The greater the frequency of clicks, or the higher the count rate, the more
radiation the Geiger-Müller tube is absorbing
o Therefore, it matters how close the tube is to the radiation source
o The further away from the source, the lower the count rate detected

A Geiger-Müller tube (or Geiger counter) is a common type of radiation detector

Background radiation
 It is important to remember that radiation is a natural phenomenon
 Radioactive elements have always existed on Earth and in outer space
 However, human activity has added to the amount of radiation that humans are
exposed to on Earth

 Background radiation is defined as:

The radiation that exists around us all the time

 Every second of the day there is some radiation emanating from natural
sources such as:
o Rocks
o Cosmic rays from space
o Foods

Chart of Background Radiation Sources

 Background radiation is the radiation that is present all around in the
environment. Radon gas is given off from some types of rock

 There are two types of background radiation:

o Natural sources
o Artificial (man-made) sources

Natural Sources of Background Radiation

Radon gas from rocks and buildings

 Airborne radon gas comes from rocks in the ground, as well as building materials
e.g. stone and brick
 This is due to the presence of radioactive elements, such as uranium,
which occur naturally in small amounts in all rocks and soils
o Uranium decays into radon gas, which is an alpha emitter
o This is particularly dangerous if inhaled into the lungs in large quantities

 Radon gas is tasteless, colourless and odourless so it can only be detected using
a Geiger counter
 Levels of radon gas are generally very low and are not a health concern, but they
can vary significantly from place to place

Cosmic rays from space

 The sun emits an enormous number of protons every second

 Some of these enter the Earth’s atmosphere at high speeds
 When they collide with molecules in the air, this leads to the production of
gamma radiation
  Other sources of cosmic rays are supernovae and other high energy cosmic
events

Carbon-14 in biological material

 All organic matter contains a tiny amount of carbon-14

 Living plants and animals constantly replace the supply of carbon in their
systems hence the amount of carbon-14 in the system stays almost constant

Radioactive material in food and drink

 Naturally occurring radioactive elements can get into food and water since they
are in contact with rocks and soil containing these elements
 Some foods contain higher amounts such as potassium-40 in bananas
 However, the amount of radioactive material is minuscule and is not a cause for
concern

Artificial Sources of Background Radiation

Nuclear medicine

 In medical settings, nuclear radiation is utilised all the time

 For example, X-rays, CT scans, radioactive tracers, and radiation therapy all use
radiation

Nuclear waste

 While nuclear waste itself does not contribute much to background radiation, it
can be dangerous for the people handling it

Nuclear fallout from nuclear weapons

 Fallout is the residue radioactive material that is thrown into the air after a
nuclear explosion, such as the bomb that exploded at Hiroshima
 While the amount of fallout in the environment is presently very low, it would
increase significantly in areas where nuclear weapons are tested

Nuclear accidents

 Nuclear accidents, such as the incident at Chornobyl, contribute a large dose of

radiation to the environment
 While these accidents are now extremely rare, they can be catastrophic and
render areas devastated for centuries

Accounting for background radiation

  Background radiation must be accounted for when taking readings in a laboratory
 This can be done by taking readings with no radioactive source present and then
subtracting this from readings with the source present
 This is known as the corrected count rate

Measuring background count rate

The background count rate can be measured using a Geiger-Müller (GM) tube
with no source present

 For example, if a Geiger counter records 24 counts in 1 minute when no source

is present, the background radiation count rate would be:
o 24 counts per minute (cpm)
o 24/60 = 0.4 counts per second (cps)

Measuring the corrected count rate of a source

The corrected count rate can be determined by measuring the count rate of a
source and subtracting the background count rate

 Then, if the Geiger counter records, for example, 285 counts in 1 minute when a
source is present, the corrected count rate would be:
o 285 − 24 = 261 counts per minute (cpm)
o 261/60 = 4.35 counts per second (cps)

 When measuring count rates, the accuracy of results can be improved by:
o Repeating readings and taking averages
o Taking readings over a long period of time

Activity & decay

  Objects containing radioactive nuclei are called sources of radiation
 Sources of radiation decay at different rates which are defined by their activity
 The activity of a radioactive source is defined as:

The rate at which the unstable nuclei decay

 Activity is measured in becquerels

o The symbol for Becquerels is Bq

 1 Becquerel is equal to 1 nucleus in the source decaying in 1 second

How does activity vary with time?

 The activity of a radioactive source decreases with time

o This is because each decay event reduces the overall number of radioactive
particles in the source

 Radioactive decay is a random process

 The randomness of radioactive decay can be observed by measuring the count rate of a
source using a Geiger-Muller (GM) tube
 When the count rate is plotted against time, fluctuations can be seen
 These fluctuations provide evidence for the randomness of radioactive decay


 The decreasing activity of a source can be shown on a graph against time.
The fluctuations show the randomness of radioactive decay
Half life
 It is impossible to know when a particular unstable nucleus will decay
 It is possible to find out the rate at which the activity of a sample decreases
o This is known as the half-life

 Half-life is defined as:

The time it takes for the number of nuclei of a sample of radioactive isotopes to
decrease by half
  In other words, the time it takes for the activity of a sample to fall to half its
original level
 Different isotopes have different half-lives and half-lives can vary from a fraction
of a second to billions of years in length

Measuring half life

 To determine the half-life of a sample, the procedure is:

o Measure the initial activity A0 of the sample
o Determine the half-life of this original activity
o Measure how the activity changes with time

 The time taken for the activity to decrease to half its original value is the half-life

Calculating half-life
 Scientists can measure the half-lives of different isotopes accurately
 Uranium-235 has a half-life of 704 million years
o This means it would take 704 million years for the activity of a uranium-
235 sample to decrease to half its original amount

 Carbon-14 has a half-life of 5700 years

o So after 5700 years, there would be 50% of the original amount of carbon-
14 remaining
o After two half-lives or 11 400 years, there would be just 25% of the
carbon-14 remaining

 With each half-life, the amount remaining decreases by half

A graph can be used to make half-life calculations

 The graph shows how the activity of a radioactive sample changes over time.
Each time the original activity halves, another half-life has passed

 The time it takes for the activity of the sample to decrease from 100% to 50% is
the half-life
 It is the same length of time as it would take to decrease from 50% activity to
25% activity
 The half-life is constant for a particular isotope

 The following table shows that as the number of half-life increases, the proportion
of the isotope remaining halves

Half life calculation table

Uses of radioactivity
 Radioactivity has many uses, such as:
o Smoke detectors (alarms)
o Monitoring the thickness of materials
o Medical procedures including diagnosis and treatment of cancer
o Sterilising food (irradiating food)
o Sterilising medical equipment
o Determining the age of ancient artefacts

 The properties of the different types of radiation determine which one is used in a
particular application
Smoke detectors

 Alpha particles are used in smoke detectors

 The alpha radiation will normally ionise the air within the detector, creating a
current
 The alpha emitter is blocked when smoke enters the detector
 The alarm is triggered by a microchip when the sensor no longer detects alpha

When no smoke is present, alpha particles ionise the air and cause a current to
flow. When smoke is present, alpha particles are absorbed and current is
prevented from flowing which triggers the alarm

Measuring the thickness of materials

  When a material, such as aluminium foil, moves above a beta source, some beta
particles will be absorbed, but most will penetrate
o The amount of beta particles passing through the material can be
monitored using a detector

 If the material gets thicker, more particles will be absorbed, and the count rate
will decrease
 If the material gets thinner, fewer particles will be absorbed, and the count rate
will increase
 This allows the manufacturer to make adjustments to keep the thickness of the
material constant

Beta particles can be used to measure the thickness of thin materials such as
paper, cardboard or aluminium foil

 Beta radiation is used because the material will only partially absorb it
o If an alpha source were used, all alpha particles would
be absorbed regardless of material thickness
o If a gamma source were used, almost all gamma rays would
be detected regardless of material thickness

Diagnosis and treatment of cancer

 Radiotherapy is the name given to the treatment of cancer using radiation

o Note: this is different to chemotherapy which is a drug treatment for
cancer

 Although radiation can cause cancer, it is also highly effective at treating it

 Ionising radiation can kill living cells
o Some cells, such as bacteria and cancer cells, are more susceptible to
radiation than others

 Beams of gamma rays are directed at the cancerous tumour

o Gamma rays are used as they can penetrate the body and reach the
tumour
 o The beams are moved around to minimise harm to healthy tissue whilst
still being aimed at the tumour

 A tracer is a radioactive isotope that can be used to track the movement of

substances, like blood, around the body
 A PET scan can detect the emissions from a tracer to diagnose cancer and
determine the location of a tumour

Radiation therapy is a type of cancer treatment which targets the tumour with
ionising radiation

Sterilising food and medical equipment

 Gamma radiation is widely used to sterilise medical equipment

 Gamma is most suited to this because:
o It is the most penetrating out of all the types of radiation
o It is penetrating enough to irradiate all sides of the instruments
o Instruments can be sterilised without removing the packaging

 Food can be irradiated in order to kill any microorganisms that are present on it
 This makes the food last longer and reduces the risk of food-borne infections

Food that has been irradiated carries this symbol, called the Radura. Different
countries allow different foods to be irradiated

Contamination & irradiation

Contamination
  Contamination is defined as:

The accidental transfer of a radioactive substance onto or into a material

 A substance is only radioactive if it contains a source of ionising radiation

 Contamination occurs when a radioactive isotope gets onto a material where it
should not be
o It is almost always a mistake or an accident e.g. a radiation leak
 As a result of this, the small amounts of the isotope in the contaminated areas
will emit radiation and the material becomes radioactive

Irradiation

 Irradiation is defined as:

The process of exposing a material to ionising radiation

 Irradiating a substance does not make it radioactive

o However, it can kill living cells

 Irradiation is usually a deliberate process, such as in the sterilisation of food or

medical equipment
o Surgical equipment is irradiated before being used in order to kill any
micro-organisms on it before surgery
o Food can be irradiated to kill any micro-organisms within it to make it last
longer

This sign is the international symbol indicating the presence of a radioactive

material

Protection from irradiation and contamination

 Radiation can mutate DNA in cells and cause cancer through both irradiation and
contamination
o Therefore, it is important to reduce the risk of exposure to radiation

 Contamination is particularly dangerous if a radioactive source gets inside the

human body
 o For example, through the inhalation of radioactive gas particles, or
ingesting contaminated food
o The internal organs will be irradiated as the source emits radiation as it
moves through the body

 To prevent irradiation, shielding can be used to absorb radiation

o Lead-lined suits are used to reduce irradiation for people working with
radioactive materials
o The lead absorbs most of the radiation that would otherwise hit the person

 To prevent contamination, an airtight suit is worn by people working in an area

where a radioactive source may be present
o This prevents radioactive atoms from getting on or into the person

Lead shielding is used when a person is getting an x-ray, as well as for people
who work with radiation. Contamination carries much greater risks than
irradiation

Differences between irradiation and contamination

 The differences between irradiation and contamination are summarised in the

table below:

Comparison of irradiation and contamination table

Irradiation Contamination
descriptio when an object is exposed to a source of when an object becomes radioactive due to the presence of a
n radiation but does not become radioactive source of radiation
exposure to source of radiation outside the
source exposure to source on or within the object
object
radiation cannot be blocked once an object is contaminated, but
prevention blocked by using shielding such as lead
can be prevented by handling the source safely
causes caused by the deliberate exposure to radiation caused by the accidental transfer of radioactive material
Dangers of radiation
  All types of ionising radiation pose a danger if mishandled as they can
o damage living cells and tissues
o cause mutations which can lead to cancer

Effect of radiation on a living cell

Ionising radiation can cause damage to DNA. Sometimes the cell can
successfully repair the DNA, but incorrect repairs can cause a mutation

 Highly ionising types of radiation are more dangerous inside the body (if a
radioactive source is somehow ingested)
o Alpha sources are the most ionising, so they are likely to cause the most
harm to living cells inside the body
o Gamma sources are the least ionising (about 20 times lower than alpha
particles), so they are likely to cause the least harm to living cells inside
the body

 Highly penetrating types of radiation are more dangerous outside the body
o Gamma sources are the most penetrating, so they are able to pass
through the skin and reach living cells in the body
o Alpha sources are least penetrating, so they would be absorbed by the
air before even reaching the skin

Safe handling of radioactive sources

 The risks of radiation exposure can be minimised by

o handing sources of radiation safely
o monitoring exposure to radiation

 To minimise the risks of contamination, safety practices must be followed, such

as:
o keeping radioactive sources in a shielded container when not in use, for
example, a lead-lined box
o wearing gloves and using tongs to handle radioactive materials
 o wearing protective clothing (particularly if the risk of inhalation or
ingestion is high)
o limiting the time that a radioactive source is outside of its container

 To minimise the risks of irradiation to workers, it is important to monitor their

exposure to radiation
o To protect against over-exposure, the dose received by different activities
is measured
o A dosemeter measures the amount of radiation in particular areas and is
often worn by radiographers, or anyone working with radiation

Badge for monitoring radiation exposure

A dosemeter, or radiation badge, can be worn by a person working with radiation

in order to keep track of the amount of radiation they are receiving

Disposal of nuclear waste

 Nuclear waste must be treated appropriately, depending on the type of radiation

it emits
o Alpha-emitting nuclear waste is easily stored in plastic or metal canisters
o Beta-emitting nuclear waste is stored inside metal canisters and concrete
silos
o Gamma-emitting nuclear waste requires storage inside lead-lined, thick
concrete silos

 Radioactive waste of all types tends to emit dangerous levels of radiation for
many years, so it must be stored securely for a very long time
 Typically, waste with the highest levels of radioactivity must be buried
underground in secure, geologically stable locations

Dealing with radioactive waste

 Depending on the type of radiation emitted, nuclear waste is treated in different
ways

 Sources with long half-lives present a risk of contamination for a much longer
time
 Radioactive waste with a long half-life can be buried underground to prevent
radioactive from being released into the environment
 Radioactive waste must be stored in strong containers
o The containers must be able to withstand harsh conditions over long
periods

 Containers must be designed to resist rust and corrosion

o Rust-proof containers are often expensive and challenging to manufacture

 The disposal site must have high security to prevent unauthorised access
 The location of the disposal site must have a low risk of natural disasters, e.g.
earthquakes
 Carefully selecting the site and using strong containers will help prevent
radioactive waste from leaking into groundwater
 Radioactive waste can also be diluted in large volumes of seawater
o This helps to minimise the concentration of radioactive materials

Nuclear energy
 The nucleus of an atom contains a huge amount of nuclear energy
o When harnessed safely, nuclear energy can significantly reduce our
dependency on fossil fuels
o However, it also has the potential to be highly destructive (nuclear
weapons, for example)

 Sources of nuclear energy include:

o Nuclear fusion
o Nuclear fission
o Radioactive decay

Nuclear fusion
  Nuclear fusion is when:

Two small nuclei join together to produce a larger nucleus

 Nuclear fusion does not happen on Earth naturally, but it does in stars
o However, fusion has been achieved on Earth, and fusion reactors are
currently in development

 When deuterium and tritium nuclei (isotopes of hydrogen) fuse, they form
a helium nucleus with the release of energy
 The amount of energy released during nuclear fusion is huge:
o The energy from 1 kg of hydrogen that undergoes fusion is equivalent to
the energy from burning about 10 million kilograms of coal

The fusion of deuterium and tritium to form helium with the release of energy

Nuclear fission

 Nuclear fission is when:

One large nucleus splits into two smaller nuclei

 The large nucleus that splits is often referred to as the parent nucleus
o The smaller nuclei that are produced are referred to as
the daughter nuclei

 This is the process used to generate electricity in nuclear power stations

 The fission of a nucleus, such as uranium, to produce smaller daughter nuclei
with the release of energy
 anium-235 nucleus absorbs a neutron and becomes uranium-236
 Uranium-236 is very unstable and splits by nuclear fission almost immediately to
produce
o two smaller daughter nuclei
o two or three neutrons

When a uranium-235 nucleus is struck by a neutron, it breaks into two smaller

daughter nuclei and 2 or 3 neutrons
Products of fission
 During fission, when a neutron collides with an unstable nucleus, the nucleus splits into
o two smaller nuclei (daughter nuclei)
o two or three neutrons
o gamma rays are also emitted

 One of the many decay reactions uranium-235 can undergo is shown below:
 When fission is induced in a uranium-235 nucleus it may split into two smaller daughter
nuclei, such as barium-144 and krypton-89

 The products of the fission reaction move away very quickly

 This is because energy is transferred from the nuclear potential energy stored in the
original nucleus into the kinetic energy of the products
 In a nuclear power station, this energy can be harnessed and converted into electrical
energy

Chain reactions
 Only one extra neutron is required to induce fission in a uranium-235 nucleus
 During the fission, it produces two or three neutrons which move away at high
speed
 Each of these new neutrons can start another fission reaction, which again emits
further neutrons
o This process can start a chain reaction

 A chain reaction occurs when

A neutron emitted from the splitting of a nucleus causes further nuclei to split
and the neutrons emitted from these cause further fission reactions

 Controlling chain reactions is an important part of the fission process in nuclear

reactors
 For a chain reaction to be maintained, there must be a minimum amount of fissile
material called the critical mass
o If the mass of fissile material exceeds the critical mass, the rate of reaction
accelerates
o This can cause a huge and uncontrolled release of energy, i.e. a nuclear
explosion
 The neutrons released by each fission reaction can go on to create further
fissions, like a chain that is linked several times – from each chain comes two
more
Control rods & moderators
 In a nuclear reactor, a chain reaction is required to keep the reactor running
 When the reactor is producing energy at the required rate, two factors must be
controlled:
o The number of free neutrons in the reactor
o The energy of the free neutrons

 The main components of a nuclear reactor are:

o control rods
o a moderator

Nuclear reactor diagram

The overall purpose of the reactor is to control chain reactions and collect the
heat energy produced from nuclear reactions to generate electricity
Control rods

Purpose of control rods: To absorb neutrons

 Control rods are made of a material which absorbs neutrons without becoming
dangerously unstable themselves
 The number of neutrons absorbed is controlled by varying the depth of the
control rods in the reactor core
o Lowering the rods further decreases the rate of fission, as more neutrons
are absorbed
o Raising the rods increases the rate of fission, as fewer neutrons are
absorbed

 This is adjusted automatically so that exactly one fission neutron produced by

each fission event goes on to cause another fission
 In the event the nuclear reactor needs to shut down, the control rods can be
lowered all the way so no reactions can take place

Moderator

Purpose of a moderator: To slow down neutrons

 The moderator is a material that surrounds the fuel rods and control rods inside
the reactor core
 The fast-moving neutrons produced by the fission reactions slow down by
colliding with the molecules of the moderator, causing them to lose some
momentum
 The neutrons are slowed down so that they are in thermal equilibrium with the
moderator
o These neutrons are called thermal neutrons
o This ensures neutrons can react efficiently with the uranium fuel

Shielding
Purpose of shielding: To absorb hazardous radiation

 The entire nuclear reactor is surrounded by shielding materials

 The daughter nuclei formed during fission, and the neutrons emitted, are
radioactive
 The reactor is surrounded by a steel and concrete wall that can be nearly 2
metres thick
 This absorbs the emissions from the reactions and ensures that the environment
around the reactor is safe for workers
 Shielding materials around a nuclear reactor are designed to absorb harmful
radiation
Fusion
 Small nuclei can react to release energy in a process called nuclear fusion
 Nuclear fusion is defined as:

When two light nuclei join to form a heavier nucleus

 This process requires extremely high temperatures to maintain

o This is why nuclear fusion has proven very hard to reproduce on Earth

 Stars, including the Sun, use nuclear fusion to produce energy

o Therefore, fusion reactions are very important to life on Earth

 In most stars, hydrogen atoms are fused together to form helium and produce
lots of energy

Two hydrogen nuclei are fusing to form a helium nuclei

 The energy produced during nuclear fusion comes from a very small amount of
the particle’s mass being converted into energy
 The amount of energy released during nuclear fusion is huge
o The energy from 1 kg of hydrogen that undergoes fusion is equivalent to
the energy from burning about 10 million kilograms of coal
 Fusion vs fission
 The following table summarises some of the key differences between fusion and
fission:

Comparison of fusion and fission table

Fusion Fission
the process of... nuclei joining together nuclei splitting
nuclei are small e.g. hydrogen large e.g. uranium
occurs in stars nuclear reactors
a large amount of energy
a large amount of energy
produces smaller daughter nuclei (usually unstable and radioactive)
larger nuclei (usually stable and not radioactive)
2 or 3 neutrons
very high temperatures
requires thermal neutrons to induce fission
very high pressures
 Nuclear fission reactors are an increasingly common method of electricity
generation on Earth
 Nuclear fusion reactors are not yet a commercially viable method for generating
electricity, but they are in development
 In the future, fusion reactors are likely to have several advantages over fission
reactors

Advantages of fusion reactors

 Nuclear fusion reactions are capable of generating more energy than fission
reactions (per kilogram of fuel)
 The nuclear fuel required for fusion (isotopes of hydrogen found in water) is
more abundant than the fuel required for fission (uranium and plutonium)
 Nuclear fusion produces no long-lived nuclear waste products

Disadvantage of fusion reactors

 The conditions for nuclear fusion are much harder to achieve and maintain on
Earth than fission

Fusion in stars
 Stars are huge balls of (mostly) hydrogen gas

 In the centre of a star, hydrogen nuclei undergo nuclear fusion to form helium
nuclei
  An equation for a possible fusion reaction is:

The outwards and inwards forces within a star are in equilibrium. The centre red
circle represents the star's core and the orange circle represents the star's outer
layers

 In larger stars where the temperature gets hot enough, helium nuclei can fuse
into heavier elements

The conditions for fusion

 Nuclear fusion requires
o extremely high temperatures
o extremely high pressures

 These conditions are required because of the electrostatic repulsion between

protons
o Since protons have a positive charge, they repel each other
o Therefore, to overcome this repulsion, protons must have very high
kinetic energies to allow them to get close enough to fuse
Hydrogen nuclei are positively charged protons which repel one another, making
it difficult to achieve fusion under normal conditions

 For hydrogen nuclei to travel at such speeds, the gas has to be heated to millions
of degrees Celsius
o Such high temperatures are usually only achievable in the cores of stars

 In regular conditions, such as on Earth, the possibility of collisions between

nuclei which result in fusion is very low
o To increase the number of collisions (and hence fusion reactions) that
occur between nuclei, high densities (and hence pressures) are also
needed

Planets, stars & galaxies

The Universe

 The Universe is defined as

A large collection of billions of galaxies

 It is also the name given to the entirety of space

Galaxies

 A galaxy is defined as

A large collection of billions of stars

 Stars are large astronomical objects such as the Sun

The Solar System

 Stars may be a part of a planetary system

o In a planetary system, planets and other astronomical objects orbit around
a star at the centre
  Our Solar System is in the Milky Way galaxy
 The Sun is at the centre of our Solar System
 Our planet, the Earth, is the third of eight planets in our Solar System

Hierarchy of the Solar System

The Universe is a large collection of galaxies and a galaxy is a large collection of
stars. The Sun is a star at the centre of our Solar System in the Milky Way galaxy

Gravitational field strength

 The strength of gravity on different planets affects an object's weight on that
planet
 Weight is defined as:

The force acting on an object due to gravitational attraction

 Planets have strong gravitational fields

o Hence, they attract nearby masses with a strong gravitational force

 The force of weight is responsible for:

o objects staying firmly on the ground
o objects always falling to the ground
o satellites being kept in orbit

Objects are attracted towards the centre of the Earth due to its gravitational field
strength
 Weight and gravitational field strength both vary on the different objects in the
Solar System
o The greater the mass of the planet then the greater its gravitational field
strength
o A higher gravitational field strength means a larger attractive force towards
the centre of that planet or moon

 The value of g varies with the distance from a planet, but on the surface of the
planet, it is roughly the same
 However, the value of g varies dramatically for different planets and moons

 The gravitational field strength (g) on the Earth is approximately 10 N/kg

 The gravitational field strength on the surface of the Moon is less than on the
Earth
o This means it would be easier to lift a mass on the surface of the Moon
than on the Earth

 The gravitational field strength on the surface of the gas giants (e.g. Jupiter and
Saturn) is more than on the Earth
o This means it would be harder to lift a mass on the gas giants than on the
Earth

Value for g on the different objects in the Solar System

 The mass of an object is always the same, but its weight changes depending on
the gravitational field
o This means that on both Earth and Jupiter, an object’s mass will have
the same value
o However, their weight will be a lot greater on Jupiter than on Earth, so
much so that a human would not be able to stand up on the surface of
Jupiter
A person’s weight on Jupiter would be so large a human would be unable to fully
stand up
Orbital motion
 The Solar System is made up of many bodies which orbit around other bodies
 The orbiting bodies in the Solar System are shown in the table below:

Table of orbiting bodies in the Solar System

orbiting body body it orbits

planet the Sun
moon planet
comet the Sun
asteroid the Sun
artificial satellites the Earth

 Smaller bodies orbit around larger bodies

o For example, planets orbit the Sun

 Orbital motion is a result of the gravitational force of attraction acting between

two bodies
 This gravitational force
o always acts towards the centre of the larger body
o causes the orbiting body to move in a circular path
 The gravitational force of attraction causes the Moon to orbit around the Earth
Differences in orbits
Orbital motion of planets

 There are several similarities in the way different planets orbit the Sun:
o Their orbits are all slightly elliptical (stretched circles) with the Sun at
one focus (approximately the centre of the orbit)
o They all orbit in the same plane
o They all travel in the same direction around the Sun

 There are also a few differences:

o They orbit at different distances from the Sun (different orbital radius)
o They orbit at different speeds
o They all take different amounts of time to orbit the Sun

 The further away a planet is from the Sun, the slower it travels and therefore
the longer it takes to orbit

The planets closest to the Sun have higher orbital speeds, whereas the planets
furthest from the Sun have lower orbital speeds

Orbital motion of moons

  Moons orbit planets in a circular path
 Some planets have more than one moon
 The closer the moon is to the planet:
o the shorter the time it will take to complete each orbit
o the greater the speed of the orbit

Orbital motion of comets

 The orbits of comets are very different to those of planets:

 Their orbits are highly elliptical (very stretched) or hyperbolic
o This causes the speed of the comets to change significantly as their
distance from the Sun changes
o Not all comets orbit in the same plane as the planets and some don’t even
orbit in the same direction

 As the comet approaches the sun, its speed increases

 As it moves further away from the sun, its speed decreases

Comets follow highly elliptical orbits around the Sun

Calculating orbital period
 When planets move around the Sun, or a moon moves around a planet, they
orbit in circular motion
o This means that in one orbit, a planet travels a distance equal to the
circumference of a circle (the shape of the orbit)
o This is equal to 2πr, where r is the radius a circle
 The relationship between speed, distance and time is:
  This orbital period (or time period) is defined as:

The time taken for an object to complete one orbit

 The orbital radius r is always taken from the centre of the object being orbited to
the object orbiting

Orbital radius and orbital speed of a planet moving around a Sun

Classification of stars
 Stars come in a wide range of sizes and colours, from yellow stars to red dwarfs,
from blue giants to red supergiants
o These can be classified according to their colour

 Warm objects emit infrared and extremely hot objects emit visible light as well
o Therefore, the colour they emit depends on how hot they are

 A star's colour is related to its surface temperature

o A red star is the coolest (at around 3000 K)
o A blue star is the hottest (at around 30 000 K)
Star colour and surface temperature

The colour of a star correlates to its temperature. The bluer the star, the hotter its
surface temperature. The redder the star, the cooler its surface temperature

 Astronomical objects cool as they expand and heat up as they contract

o This means that their colour will also change according to their surface
temperature

 When a star becomes a red giant it becomes redder as it expands and cools
 When a star becomes a white dwarf it becomes whiter as it contracts and heats
up

The life cycle of solar mass stars

 All stars, including the Sun, began as a cloud of dust and gas
 Once a star has formed, it will spend its life going through a sequence of
evolutionary stages, known as the life cycle of a star

Summary of the life cycles of stars

Flow diagram showing the life cycle of a star which is the same size as the Sun
(solar mass) and the lifecycle of a star which is much more massive than the Sun
Star formation

 All stars follow the same initial stages:

Nebula → protostar → main sequence star

Nebula

 Stars form from a giant interstellar cloud of gas and dust called a nebula

Protostar

 The force of gravity within a nebula pulls the particles closer together until a hot
ball of gas forms, known as a protostar
 As the particles are pulled closer together the density of the protostar
will increase
 This results in more frequent collisions between the particles which causes
the temperature to increase

Main sequence star

 Once the protostar becomes hot enough, nuclear fusion reactions occur within
its core
 Once a star initiates fusion, it is known as a main-sequence star
 During the main sequence, the star is in equilibrium and said to be stable

The life cycle of a solar mass star

 After the main sequence, a low-mass star finishes its life cycle in the following
evolutionary stages:

Red giant → planetary nebula → white dwarf

Red giant

 After several billion years, the hydrogen causing the fusion reactions in the star
will begin to run out
 Once this happens, the fusion reactions in the core will start to die down
 The star will begin to fuse helium which causes the outer part of the star
to expand
 As the star expands, its surface cools and it becomes a red giant

White dwarf

 Once the helium fusion reactions have finished, the star collapses and becomes
a white dwarf
  The white dwarf cools down over time and as a result, the amount of energy it
emits decreases

The life cycle of a low-mass star

The life cycle of a star that is similar to our Sun

The life cycle of larger stars
 After the main sequence, a high-mass star finishes its life cycle in the following
evolutionary stages:

Red supergiant → supernova → neutron star (or black hole)

 The key differences between a lower mass and higher mass star at this stage
are:
o A higher mass star will stay on the main sequence for a shorter
time before it becomes a red supergiant
o A lower mass star fuses helium into heavy elements, such as carbon,
whereas a higher mass star fuses helium into even heavier elements,
such as iron

Red supergiant

 After several million years, the hydrogen causing the fusion reactions in the star
will begin to run out
 Once this happens, the fusion reactions in the core will start to die down
 The star will begin to fuse helium which causes the outer part of the star
to expand
 As the star expands, its surface cools and it becomes a red supergiant
Supernova

 Once the fusion reactions inside the red supergiant cannot continue, the core of
the star will collapse suddenly and cause a gigantic explosion called
a supernova
 At the centre of this explosion, a dense body called a neutron star will form
 The outer remnants of the star are ejected into space forming new clouds of
dust and gas (nebula)
o The heaviest elements are formed during a supernova, and these are
ejected into space
o These nebulae may form new planetary systems

Neutron star (or black hole)

 In the case of the most massive stars, the neutron star that forms at the centre
will continue to collapse under the force of gravity until it forms a black hole
 A black hole is an extremely dense point in space that not even light can
escape from

The life cycle of a high-mass star

The life cycle of a star much larger than our Sun

Absolute magnitude
Luminosity

 The luminosity of a star is defined as

The total amount of light energy emitted by the star

  Luminosity is a measure of a star's brightness or power output

Apparent magnitude

 The brightness, or apparent magnitude, of a star depends on two main factors:

o the luminosity of the star
o the distance the star is from Earth (more distant stars are usually fainter
than nearby stars)

 Apparent magnitude is defined as

The perceived brightness of a star as seen from Earth

 The apparent magnitude scale runs back to front:

o the brighter the star, the lower the magnitude
o the dimmer the star, the higher the magnitude

The apparent magnitude scale

Examples of the apparent magnitude of different astronomical bodies

Absolute magnitude

 Astronomers describe the brightness of stars at a standard distance using

the absolute magnitude scale
 o a bright star which is far away can look the same as a dim star which is
nearby
o therefore, it is difficult to measure the brightness of stars directly

 Absolute magnitude is defined as

A measure of how bright stars would appear if they were all placed the same
distance away from the Earth

 The standard distance astronomers use is 10 parsecs, 32.6 light-years or 3.04 ×

1014 km away from the Earth

Hertzsprung-Russell diagrams
 The properties of stars can be classified using the Hertzsprung-Russell (HR)
diagram
 This is a plot of luminosity on the y-axis and temperature on the x-axis
 Usually, it is given in solar units, where the luminosity of the Sun = 1, so
o For stars which are brighter than the Sun, luminosity > 1
o For stars which are dimmer than the Sun, luminosity < 1

 Surface temperature is measured in kelvin (K) and is plotted backwards from

hottest to coolest
 It can also be displayed as a colour where
o The hottest stars are blue
o The coolest stars are red

The Hertzsprung-Russell diagram

 The Hertzsprung-Russell (HR) diagram is a way of displaying the properties of
stars and representing their life cycles

 The key areas of the H-R diagram are:

o The brightest stars (high luminosity) are found near the top
o The dimmest stars (low luminosity) are found near the bottom
o The hottest stars (high temperature) are found towards the left
o The coolest stars (low temperature) are found towards the right

 The life cycle of a star can be shown on a Hertzsprung-Russell diagram

 The main features of the Hertzsprung-Russell diagram are:
o Most stars are found to lie on the main sequence. This is the band of
stars going from top left to bottom right
o Below the main sequence (and slightly to the left) are the white dwarfs
o Above the main sequence on the right-hand side are the red giants
o Directly above the red giants are the red supergiants

 This means that

o The hottest, brightest stars are the largest main sequence stars, also
called supergiant stars
o The coolest, brightest stars are red supergiants
o The hottest, dimmest stars are white dwarfs
o the coolest, dimmest stars are the smallest main sequence stars, also
called red dwarfs

The Big Bang theory

 Around 14 billion years ago, the Universe began from a very small region that
was extremely hot and dense
 Then there was a giant explosion, which is known as the Big Bang
 This caused the universe to expand from a single point, cooling as it does so, to
form the universe today
 Each point expands away from the others
o This is seen from galaxies moving away from each other, and the further
away they are the faster they move
 As a result of the initial explosion, the Universe continues to expand

All galaxies are moving away from each other, indicating that the universe is
expanding

 An analogy of this is points drawn on a balloon where the balloon represents

space and the points as galaxies
 When the balloon is deflated, all the points are close together and an equal
distance apart
 As the balloon expands, all the points become further apart by the same
amount
 This is because the space itself has expanded between the galaxies
o Therefore, the density of galaxies falls as the Universe expands
 A balloon inflating is similar to the stretching of the space between galaxies
Evidence for the Big Bang
What are two pieces of evidence that support the Big Bang theory?

 Since there is more evidence supporting the Big Bang theory than the Steady
State theory, it is the currently accepted model for the origin of the Universe
 The two main pieces of evidence supporting the Big Bang are
o Galactic red-shift
o Cosmic Microwave Background (CMB) radiation

Evidence from galactic red-shift

 By observing the light spectrums from supernovae in other galaxies there is

evidence to suggest that distant galaxies are receding (moving further apart)
even faster than nearby galaxies
o These observations were first made in 1998

 The light spectrums show that light from distant galaxies is redshifted, which is
evidence that the universe is expanding
 As a result, astronomers have concluded that:
o All galaxies are moving away from the Earth
o Galaxies are moving away from each other

 This is what is expected after an explosion

o Matter is first densely packed and as it explodes it, it moves out
in all directions getting further and further from the source of the explosion
o Some matter will be lighter and travel at a greater speed, further from
the source of the explosion
 o Some matter will be heavier and travel at a slower speed, closer to the
source of the explosion

 If someone were to travel back in time and compare the separation distance of
the galaxies:
o It would be seen that galaxies would become closer and closer
together until the entire universe was a single point
 If the galaxies were originally all grouped together at a single point and were
then exploded a similar effect would be observed
o The galaxies that are the furthest are moving the fastest - their distance
is proportional to their speed
o The galaxies that are closer are moving slower

Tracing the expansion of the universe back to the beginning of time leads to the
idea the universe began with a “big bang”

Evidence from CMB radiation

 The discovery of the CMB (Cosmic Microwave Background) led to the Big Bang
theory becoming the currently accepted model
o The CMB is a type of electromagnetic radiation which is a remnant from
the early stages of the Universe
o It has a wavelength of around 1 mm making it a microwave, hence the
name Cosmic Microwave Background
 In 1964, Astronomers discovered radiation in the microwave region of the
electromagnetic spectrum coming from all directions and at a generally uniform
temperature of 2.73 K
o They were unable to do this any earlier since microwaves
are absorbed by the atmosphere
o Around this time, space flight was developed which enabled astronomers
to send telescopes into orbit above the atmosphere

 According to the Big Bang theory, the early Universe was an

extremely hot and dense environment
o As a result of this, it must have emitted thermal radiation

 The radiation is in the microwave region

o This is because over the past 14 billion years or so, the radiation initially
from the Big Bang has become redshifted as the Universe has expanded
o Initially, this would have been high energy radiation, towards the gamma
end of the spectrum
o As the Universe expanded, the wavelength of the radiation increased
o Over time, it has increased so much that it is now in
the microwave region of the spectrum

The CMB is a result of high energy radiation being redshifted over billions of
years

 The CMB radiation is very uniform and has the exact profile expected to be
emitted from a hot body that has cooled down over a very long time
o This phenomenon is something that other theories (such as the Steady
State Theory) cannot explain

 The CMB is represented by the following map:

 The CMB map with areas of higher and lower temperature. Places with higher
temperature have a higher concentration of galaxies, Suns and planets

 This is the closest image to a map of the Universe

 The different colours represent different temperatures
o The red / orange / brown regions represent warmer temperature
indicating a higher density of galaxies
o The blue regions represents cooler temperature indicating a lower
density of galaxies

 The temperature of the CMB is mostly uniform, however, there are minuscule
temperature fluctuations (on the order of 0.00001 K)
o This implies that all objects in the Universe are more or less uniformly
spread out

Doppler shift
 Usually, when an object emits waves, the wavefronts spread out symmetrically
o If the wave source moves, the waves can become squashed together or
stretched out
 Therefore, when a wave source moves relative to an observer there will be a
change in the observed frequency and wavelength
Wavefronts are even in a stationary object but are closer together in the direction
of the moving wave source

 A moving object will cause the wavelength, λ, (and frequency) of the waves to
change:
o The wavelength of the waves in front of the source decreases (λ – Δλ)
and the frequency increases
o The wavelength behind the source increases (λ + Δλ) and the frequency
decreases
o This effect is known as the Doppler effect or Doppler shift

 Note: Δλ means 'change in wavelength'

Calculating Doppler shift of light

 Doppler shift can be calculated using the Doppler effect equation:
  The doppler shift equation can be used to calculate the velocity of a galaxy if its
wavelength can be measured and compared to a reference wavelength

 Since the fractions have the same units on the numerator (top number) and
denominator (bottom number), the Doppler shift has no units

Galactic red-shift
 The Doppler effect affects all types of waves, including light
 Light emitted from stars and galaxies will be at a certain wavelength in the visible
part of the electromagnetic spectrum
 If an object moves away from an observer the wavelength of light increases
o This is known as redshift as the light moves towards the red end of the
spectrum
 The redshift definition is therefore:

The phenomenon of the wavelength of light appearing to increase when the

source moves away from an observer

 If an object moves towards an observer the wavelength of light decreases

o This is known as blueshift as the light moves towards the blue end of the
spectrum

Light from a star that is moving towards an observer will show blueshift and light
from a star moving away from an observer will show redshift

 An increase in wavelength (redshift) is a decrease in frequency and vice versa

 The observer in front observes a blue shift, the observer behind observes a
redshift
The expanding universe
 Galactic redshift provides evidence for the Big Bang Theory and the expansion of
the universe
 The diagram below shows the light coming to us from a close object, such as
the Sun, and the light coming to the Earth from a distant galaxy

Redshift diagram for a light spectrum

Comparing the light spectrum produced from the Sun and a distant galaxy. The
spectral lines from the distant galaxy are redshifted.

Red shift provides evidence that the Universe is expanding because:

 Red shift is observed when the spectral lines from the distant galaxy move closer
to the red end of the spectrum
o This is because light waves are stretched by the expansion of the
universe so the wavelength increases (or frequency decreases)
o This indicates that the galaxies are moving away from us

 Light spectrums produced from distant galaxies are red

shifted more than nearby galaxies
o This shows that the greater the distance to the galaxy,
the greater the redshift
o This means that the further away a galaxy is, the faster it is moving away
from the Earth

 These observations imply that the universe is expanding and

therefore support the Big Bang Theory

Graph showing the greater the distance to a galaxy, the greater the redshift